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It is shown that by means of a complex coordinate transformation performed on the monopole or Schwarzschild metric one obtains a new metric (first discovered by Kerr). It has been suggested that this metric be interpreted as that arising from a spinning particle. We wish to suggest a more complicated interpretation, namely that the metric has certain characteristics that correspond to a ring of mass that is rotating about its axis of symmetry. The argument for this interpretation comes from three separate places: (1) the metric appears to have the appropriate multipole structure when analyzed in the manner discussed in the previous paper, (2) in a covariantly defined flat space associated with the metric, the Riemann tensor has a circular singularity, (3) there exists a closely analogous solution of Maxwell's equations that has characteristics of a field due to a rotating ring of charge.

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... In this work, we establish an asymptotically flat solution for a rotating black hole in modified GR. In place of obtaining a solution from the appropriate Einstein action for a modified GR, we rely on the Newman-Janis algorithm (NJA) [8]. We know that based on NJA the Kerr black hole solution can be derived from the Schwarzschild solution by making an elementary transformation involved with complex numbers. ...

... Solving Eqs. (8) and (9), and applying the boundary condition X (r ) → 1 as r → ∞, X (r ) can be found as [4] ...

... Here "."s in Eq. (18) indicate that the metric is symmetric and will have the same elements as in the upper triangle. The contravariant form of the metric can be written so that it can be expressed in terms of its null tetrads [8,15,16] as ...

The theory of f ( R )-gravity is one of the theories of modified Einstein gravity. The vacuum solution, on the other hand, of the field equation is the solution for black hole geometry. We establish here an asymptotically flat rotating black hole solution in an f ( R )-gravity. This essentially leads to the modified solution to the Kerr black hole. This solution exhibits the change in fundamental properties of the black hole and its geometry. It particularly shows that radii of marginally stable and bound orbits and black hole event horizon increase compared to those in Einstein gravity, depending on the modified gravity parameter. It further argues for faster spinning black holes with spin (Kerr) parameter greater than unity, without any naked singularity. This supports the weak cosmic censorship hypothesis.

... With the aid of the Newman-Janis algorithm [12], the above-mentioned nonrotating black holes with the quintessence and/or the cloud of strings can be transformed to rotating black hole counterparts [13][14][15][16]. Adding the cosmological constant, the authors of [17] obtained the Kerr-Newman-AdS solutions of the Einstein-Maxwell equation in quintessence field. ...

... (2), (3), (12), and (13), two components of the metric for the description of the Schwarzschild black hole surrounded by the quintessence and the cloud of strings can be written in [10] as follows: ...

... In terms of the Newman-Janis algoritm [12], the Reissner-Nordström black hole metric with the quintessence and the cloud of strings can be transformed into the Kerr-Newman black hole metric in the quintessence and the cloud of strings [13][14][15][16]. Adding a cosmological constant Λ [17], the authors of [18] obtained a Kerr-Newman-AdS solution immersed in quintessence and string cloud. ...

The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The fourth motion constant and the axial symmetry of the spacetime give a chance to the existence of radial effective potentials with stable circular orbits in two-dimensional planes, such as the equatorial plane and other nonequatorial planes. They also give a possibility of the presence of radial effective potentials with stable spherical orbits in the three-dimensional space. The dynamical parameters play important roles in changing the graphs of the effective potentials. In addition, variations of these parameters affect the presence or absence of stable circular orbits, innermost stable circular orbits, stable spherical orbits, and marginally stable spherical orbits. They also affect the radii of the stable circular or spherical orbits. It is numerically shown that the stable circular orbits and innermost stable circular orbits can exist not only in the equatorial plane but also in the nonequatorial planes. Several stable spherical orbits and marginally stable spherical orbits are numerically confirmed too. In particular, there are some stable spherical orbits and marginally stable spherical orbits with vanishing angular momenta which cover the whole range of latitudinal coordinates.

... In this section, using the Newman-Janis algorithm [47] along with some modifications proposed by Azreg-Aïnou [48], we obtain the metric for a rotating charged black hole in the presence of a fluid of strings in Rastall gravity. In the sequence, we will obtain some physical quantities of interest, such as the temperature and the event horizon for this solution, as well as some trajectories of particles close to the black hole. ...

... The Newman-Janis algorithm was used originally to obtain the Kerr metric from the Schwarzschild metric through a coordinate transformation that involves allowing the radial coordinate to assume complex values. Here we will use the algorithm proposed by Newman-Janis [47], combined with some modifications presented in [48], so that we start by writing a general static metric as follows ...

... By using Equation (44) we can find the contravariant components of the metric tensor corresponding to the tetrads of Equation (47), which can then be inverted to obtain the covariant components given below g uu = −F, ...

We obtain the exact solution of the field equations in the framework of the Rastall gravity for a static, charged and spherically symmetric black hole surrounded by a fluid of strings and analyze the behavior of the horizons, mass, Hawking temperature and geodesics in terms of the parameter related to the presence of the fluid as well as on the parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} of the Rastall gravity. We discuss some particular cases and the fact that a subclass of the obtained solutions can be mapped to black hole solutions obtained in the framework of general relativity. We also obtain a class of solutions which correspond to a rotating, charged black hole surrounded by a fluid of strings, by applying an algorithm to construct rotating solutions from the static solutions. The horizons, mass, Hawking temperature, ergoregions and geodesics are examined. The role played by the presence of the fluid of strings and the characteristics arising from the Rastall gravity are emphasized.

... In the literature, some attempts along this ling have been made by adopting the Newman-Janis Algorithm (NJA) [23,24,25,26]. As a metric-generating method, NJA works quite well in generating Kerr and Kerr-Newman metrics starting with their non-rotating counterparts, called seed metrics [27]. Although it is challenging at this point to justify the validity of using NJA beyond GR, it may still allow us to construct effective models for rotating black holes, which could capture the key features that LQG black holes are supposed to have. ...

... This assumption allows us to make some quantitative statements on the phenomenology of the model. In this section, we will briefly review NJA [27] and how its revised version [28] works. ...

... wherem µ is the complex conjugate of m µ . The explicit expression of the null tetrad Z µ a is not shown here because it is not very informative (see [27,28] for the detailed expression). ...

To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman-Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature.

... In the literature, some attempts along this ling have been made by adopting the Newman-Janis Algorithm (NJA) [23,24,25,26]. As a metric-generating method, NJA works quite well in generating Kerr and Kerr-Newman metrics starting with their non-rotating counterparts, called seed metrics [27]. Although it is challenging at this point to justify the validity of using NJA beyond GR, it may still allow us to construct effective models for rotating black holes, which could capture the key features that LQG black holes are supposed to have. ...

... This assumption allows us to make some quantitative statements on the phenomenology of the model. In this section, we will briefly review NJA [27] and how its revised version [28] works. ...

... wherem µ is the complex conjugate of m µ . The explicit expression of the null tetrad Z µ a is not shown here because it is not very informative (see [27,28] for the detailed expression). ...

To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman–Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature.

... Our amplitudes-based approach to the massless limit of Kerr suggests that there should be some double copy structure in play 10 . For finite mass, the framework of classical double copy [13,93] indicates that the 'single copy' of the Kerr metric in electromagnetism is a spinning point charge, often called the √ Kerr solution [93,94]. Thus, one can naturally ask: what is the ultrarelativistic limit of √ Kerr, and is it the single copy of the ultrarelativistic limit of Kerr? ...

... As expected, at distances r > a this corresponds to an electromagnetic shockwave, while for r < a the solution describes a disc of radius a with total charge Q [94]. It is worth noting that, at least naïvely, the direct ultraboost of the source of √ Kerr obtained by amplitudes methods does not produce the same profile with finite size effects. ...

The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.

... Since astrophysical black holes are generally rotating, we shall consider the axisymmetric counterpart of the Bardeen black holes in this work. The rotating solution is obtained by applying the Newman-Janis algorithm to the static spherically symmetric spacetime [49][50][51][52]. ...

... Since astrophysical black holes are generally rotating one needs to find the rotating counterpart of Eq. (5). This is accomplished by applying the Newman-Janis algorithm to the static, spherically symmetric seed metric [49][50][51][52]. The rotating counterpart of the Bardeen metric in Boyer-Lindquist coordinates correspond to, ...

We study the prospect of Bardeen black holes in explaining the observed shadow of Sgr A* and M87*. Bardeen black holes are regular black holes endowed with a magnetic monopole charge that arise in Einstein gravity coupled to non-linear electrodynamics. These black holes are interesting as they can evade the r = 0 curvature singularity arising in general relativity. It is therefore worthwhile to look for signatures of Bardeen black holes in astrophysical observations. With two successive release of black hole images by the Event Horizon Telescope (EHT) collaboration, the scope to test the nature of strong gravity has substantially increased. We compare the theoretically computed shadow observables with the observed image of Sgr A* and M87*. Our analysis reveals that while the observed angular diameter of M87* favors the Kerr scenario, the shadow of Sgr A* can be better explained by the Bardeen background. This indicates that although rare, certain black holes exhibit a preference towards regular black holes like the Bardeen spacetime.

... Astrophysical black holes are generally rotating and since we wish to investigate the observational signatures of the aforesaid regular black hole, studying its rotating counterpart is important. Such a rotating solution is obtained by applying the Newman-Janis algorithm [44][45][46][47] to the static, spherically symmetric seed metric which has an exponential mass function. Just as the spherically symmetric solution resembles the Reissner Nörsdrom metric, the axisymmetric solution resembles the Kerr-Newman background far from the source [48]. ...

... Since astrophysical black holes are in general rotating, studying the axisymmetric counterpart of Eq. (13) is observationally more relevant. The stationary, axisymmetric and asymptotically flat black hole solution of Einstein's equations with source given by Eq. (14) is obtained by applying the Newman-Janis algorithm [44][45][46][47] to the seed metric Eq. (13) [48]. ...

With the recent release of the black hole image of Sgr A* alongside the earlier image of M87*, one can now really hope to acquire a better understanding of the gravitational physics at the horizon scale. In this paper, we investigate the prospect of the regular black hole scenario with a Minkowski core in explaining the observed shadow of M87* and Sgr A*. Regular black holes generally appear in Einstein gravity coupled to non-linear electrodynamics and are interesting as they can evade the r = 0 curvature singularity arising in general relativity. Using the previously determined mass and distance we compute the observables associated with the black hole shadow. These when compared with the observed angular diameter reveals that the shadow of M87* and Sgr A* favor the regular black hole scenario with a small but non-zero charge. The implications are discussed.

... Complex methods as a tool to investigate spacetime structure in General Relativity (GR) have a long and fruitful history of remarkable developments. Profound constructions, pioneered by Penrose, Newman, Plebański, Robinson, Trautman, [1][2][3][4][5][6] among others, include twistor theory and heavenly structures, but there are also simple yet intriguing results such as the "Newman-Janis shift" relating special solutions via complex coordinate transformations. ...

... where we assume M = 0. Thus, the Kähler potentials are related by a Newman-Janis shift r → r − ia cos θ [5], although it is not at all obvious from (19). For M = 0, which corresponds (locally) to flat spacetime, we can see the Newman-Janis shift as follows. ...

We obtain a closed formula for the Kaehler potential of a broad class of four-dimensional Lorentzian or Euclidean conformal "Kaehler" geometries, including the Plebanski-Demianski class and various gravitational instantons such as Fubini-Study and Chen-Teo. We show that the Kaehler potentials of Schwarzschild and Kerr are related by a Newman-Janis shift. Our method also shows that a class of supergravity black holes, including the Kerr-Sen spacetime, is Hermitian (but not conformal Kaehler). We finally show that the integrability conditions of complex structures lead naturally to the (non-linear) Weyl double copy, and we give new vacuum and non-vacuum examples of this relation.

... In this work, we first construct a rotating version of null naked singularity (NNS) spacetime to explore its physical features. The rotating naked singularity spacetime could be obtained by applying the Newman-Janis Algorithm (NJA) to the static NNS [47][48][49][50]. Furthermore, while applying the NJA to other spacetime metrics, such as naked singularities and other black hole solutions, the final result in Eddington-Finkelstein coordinates (EFC) may not be transformed into the Boyer-Lindquist coordinates (BLC) due to the complexification process mentioned in [51,[53][54][55]. ...

... Using Eqs. (47) and (48), we find dφ dr = (Lg tt + g tφ ) √ g rr (g tt g φφ + g 2 tφ )(−g tt L 2 − 2 Lg tφ + 2 g φφ ) ...

In this paper, we investigate the light trajectories and shadow properties in the rotating version of null naked singularity (NNS) spacetime which is derived using the Newman–Janis algorithm without complexification method. We discuss some of the geometrical properties and causal structure of Rotating Naked Singularity (RNS) spacetime. The gravitational lensing in a rotating naked singularity is analyzed, and the results are compared to those of a Kerr black hole. In the case of a Kerr black hole, the photon sphere exists for both prograde and retrograde photon orbits, whereas for RNS, the photon sphere exists only for retrograde photon orbits. As a result, the naked singularity projects an arc-shaped shadow that differs from the contour-shaped shadow cast by a Kerr black hole.

... The Newman-Janis algorithm (NJA) is a generating method for constructing rotating black hole solutions from static ones [104]. This method works well in producing Kerr black holes from Schwarzschild black holes [104] and Kerr-Newman black holes from Reissner-Nordström black holes in general relativity [105]. ...

... The Newman-Janis algorithm (NJA) is a generating method for constructing rotating black hole solutions from static ones [104]. This method works well in producing Kerr black holes from Schwarzschild black holes [104] and Kerr-Newman black holes from Reissner-Nordström black holes in general relativity [105]. However, for other spherically symmetric black holes in modified gravitational theories, their rotating counterparts obtained by using the NJA will introduce additional sources [106][107][108][109]. ...

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the nonlocal parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the nonlocal parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow becomes more deformed with the increase in the nonlocal parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the nonlocal parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase in the nonlocal parameter. In addition, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the nonlocal parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the nonlocal parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

... The procedure of eq. (65), that relates the amplitudes for the Kerr-Taub-NUT solution to those generating pure Schwarzschild, is a momentum-space counterpart of the well-known Newman-Janis shift for the corresponding classical fields [78]. Here we see a novel interpretation of this shift, namely that it acts as a frequency shift in the energy Laplace transform of the momentum-space amplitude, whose consequence is to ensure locality of the double copy in twistor space! ...

The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space and when this form will break has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.

... We note that these regular black holes are static and spherically symmetric, while the regular black holes that would exist in nature are most probably rotating and axially symmetric. For a static and spherically symmetric black hole with singularities, the Newman-Janis algorithm (NJA) can be used [12] to transform it into a rotating and axially symmetric black hole. However, for a static and spherically symmetric regular black hole without singularities, the NJA does not give a unique rotating and axially symmetric regular black hole because the complex parameterization of radial coordinates has flexibility to a certain extent [13][14][15]. ...

Regular black holes, as an important attempt to eliminate the singularities in general relativity, have been widely concerned. Due to the fact that the superradiance associated with rotating regular black holes plays an indispensable role in black hole physics, we calculate the superradiance related effects, {\em i.e.}, the superradiance instability and the energy extraction efficiency for a scalar particle with a small mass around a rotating regular black hole, where the rotating regular black hole is constructed by the modified Newman-Janis algorithm (NJA). We analytically give the eigenfrequency associated with instability and the amplification factor associated with energy extraction. For two specific models, the rotating Hayward and Bardeen black holes, we investigate how their regularization parameters affect the growth of instability and the efficiency of energy extraction from the two rotating regular black holes. We find that the regularization parameters give rise to different modes on the superradiance instability and the energy extraction when the rotation parameters are varying. There are two modes for the growth of superradiance instability, and four modes for the energy extraction. Our results show the diversity of superradiance in the competition between the regularization parameter and the rotation parameter for rotating regular black holes.

... The NJA (Newman & Janis 1965;Drake & Szekeres 2000) has been extensively used to generate rotating black hole metric from the non-rotating counterparts (Johannsen & Psaltis 2011), whereas a revised NJA (Azreg-Aïnou 2014) has been successfully applied to construct rotating black holes in MoG (Brahma et al. 2021). The rotating counterpart of the black hole (2) with (6) can be obtained by the revised NJA (Azreg-Aïnou 2014; Brahma et al. 2021) whereby, the rotating black holes in the Horndeski gravity read ...

The Event Horizon Telescope (EHT) collaboration recently unveiled the first image of the supermassive black hole M87*, which exhibited a ring of angular diameter $\theta_{d}=42 \pm 3 \mu as$, a circularity deviation $\Delta C \leq 0.1$, and also inferred a black hole mass of $M=(6.5 \pm 0.7) \times 10^9 M_\odot $. This provides a new window onto tests of theories of gravity in the strong-field regime, including probes of violations of the no-hair theorem. It is widely believed that the Kerr metric describes the astrophysical black holes, as encapsulated in the critical but untested no-hair theorem.
Modeling Horndeski gravity black holes---with additional hair parameter $h$ besides the mass $M$ and spin $a$ of the Kerr black hole---as the supermassive black hole M87*, we observe that to be a viable astrophysical black hole candidate, the EHT result constrains ($a$, $h$) parameter space. However, a systematic bias analysis indicates rotating Horndeski black hole shadows may or may not capture Kerr black hole shadows, depending
on the parameter values; the latter is the case over a substantial part of the constrained parameter space, allowing Horndeski gravity and general relativity to be distinguishable in the said space, and opening up the possibility of potential modifications to the Kerr metric.

... Since astrophysical black holes are rotating in nature it is more realistic and relevant to consider the stationary, axisymmetric counterpart of the aforesaid deformed metric. This is generally accomplished by applying the Newman-Janis algorithm [71] to the static, spherically symmetric seed metric. The Newman-Janis algorithm has some ambiguities associated with the procedure of complex coordinate transformation [72] which is circumvented by the method suggested by Azreg-Aïnou which demands that the final rotating metric must be written in the Boyer-Lindquist form and satisfy the gravitational field equations [73,74]. ...

We study the method of extended gravitational decoupling in obtaining static black hole solutions satisfying Einstein's equations with a tensor vacuum. The source has quite generic characteristics and satisfies the strong energy condition. The stationary, axisymmetric counterpart of the static metric is obtained by applying the Newman-Janis and Azreg-A\"{i}nou algorithms. The thermodynamics of the rotating solution is studied and the expressions for the entropy, Hawking temperature, and quasilocal energy are derived. The dependence of the temperature, free energy, and specific heat on the horizon radius is studied for various values of the hairy parameter and the black hole spin. Such a study reveals that small black holes are thermodynamically more stable compared to large black holes, and that rotating hairy black holes can be in thermodynamic equilibrium at larger temperatures compared to their Kerr counterpart. We further discuss the first law of black hole thermodynamics for the hairy case and discuss its implications.

... This is the Newman-Janis shift [145], appearing in electrodynamics. For this reason the solution has been termed √ Kerr. ...

Scattering amplitudes have their origin in quantum ﬁeld theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of this formalism is that it enables us to study implications of the double copy in classical gravity. We discuss examples of observables including the total change of a particle’s momentum, and the gravitational waveform, during a scattering encounter. The double copy also allows direct access to classical solutions in gravity. We review this classical double copy starting from its linearised level, where it originates in the double copy of three-point amplitudes. The classical double copy extends elegantly to exact solutions, making a connection between scattering amplitudes and the geometric formulation of General Relativity.

... To describe the scattering of massless particles with spin it is necessary to construct the spinning analogue of the Aichelburg-Sexl shockwave. A well known method for constructing a spinning solution from a non-spinning solution, most notably the Kerr metric from Schwarzschild, is the Newman-Janis transformation [46]. An analogous transformation can be applied to the Aichelburg-Sexl shockwave [47] to produce what we will refer to as the spinning gravitational shockwave 7 . ...

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

... The closest one has to a pedagogical first-principles derivation of the Kerr spacetime is via the Newman-Janis trick [25,26], developed in 1965, which was immediately used in then deriving the electro-magnetically charged Kerr-Newman spacetime [27]. Despite many valiant efforts [28][29][30][31][32][33][34][35][36][37][38] it is still fair to say that no fully convincing explanation of why the Newman-Janis trick works has been forthcoming. ...

Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr solution without significant computational effort. (Typically involving computer-aided symbolic algebra.) Perhaps the closest one gets in this regard is the Newman-Janis trick; a trick which requires several physically unmotivated choices in order to work. Herein we shall try to make some progress on this issue by using a non-ortho-normal tetrad based on oblate spheroidal coordinates to absorb as much of the messy angular dependence as possible, leaving one to deal with a relatively simple angle-independent tetrad-component metric. That is, we shall write $g_{ab} = g_{AB} \; e^A{}_a\; e^B{}_b$ seeking to keep both the tetrad-component metric $g_{AB}$ and the non-ortho-normal co-tetrad $e^A{}_a$ relatively simple but non-trivial. We shall see that it is possible to put all the mass dependence into $g_{AB}$, while the non-ortho-normal co-tetrad $e^A{}_a$ can be chosen to be a mass-independent representation of flat Minkowski space in oblate spheroidal coordinates: $(g_\mathrm{Minkowski})_{ab} = \eta_{AB} \; e^A{}_a\; e^B{}_b$. This procedure separates out, to the greatest extent possible, the mass dependence from the rotational dependence, and makes the Kerr solution perhaps a little less mysterious.

... To obtain the rotating counterpart of this black hole spacetime, in Ref. [37], a modified version of the Newman-Janis algorithm [45], proposed by Azreg-Aïnou [46] was applied. This algorithm generates the stationary spacetime ...

In this paper, we calculate the analytical solutions for the radii of planar and polar spherical photon orbits around a rotating black hole that is associated with quintessential field and cloud of strings. This includes a full analytical treatment of a quintic that describes orbits on the equatorial plane. Furthermore, The radial profile of the impact parameters is studied and the radii corresponding to the extreme cases are derived. For the more general cases, we also discuss the photon regions that form around this black hole. To simulate the orbits that appear in different inclinations, we analytically solve the latitudinal and azimuth equations of motion in terms of the Weierstrassian elliptic functions, by considering the radii of spherical orbits, in their general form, as the initial conditions. The period and the stability conditions of the orbits are also obtained analytically.

... Astrophysical black holes are generally rotating and since we wish to investigate the observational signatures of the aforesaid regular black hole, studying its rotating counterpart is important. Such a rotating solution is obtained by applying the Newman-Janis algorithm [44][45][46][47] to the static, spherically symmetric seed metric which has an exponential mass function. Just as the spherically symmetric solution resembles the Reissner Nörsdrom metric, the axisymmetric solution resembles the Kerr-Newman background far from the source [48]. ...

With the recent release of the black hole image of Sgr A* alongside the earlier image of M87*, one can now really hope to acquire a better understanding of the gravitational physics at the horizon scale. In this paper, we investigate the prospect of the regular black hole scenario with a Minkowski core in explaining the observed shadow of M87* and Sgr A*. Regular black holes generally appear in Einstein gravity coupled to non-linear electrodynamics and are interesting as they can evade the r = 0 curvature singularity arising in general relativity. Using the previously determined mass and distance we compute the observables associated with the black hole shadow. These when compared with the observed angular diameter reveal that the shadow of M87* and Sgr A* favor the regular black hole scenario with a small but non-zero charge. The implications are discussed.

... Third, the spherically symmetric counterpart of Eq. (3.1) (or similar metrics with slightly different functions in place of Eq. (3.2)) have been proposed in other approaches to quantum gravity [68][69][70][71][72][73][74][75][76]. In those cases where upgrades to spinning spacetimes were made, they typically follow the Janis-Newman algorithm [77,78]. This results in a mass-function that only depends on χ, not on r. ...

Quantum-gravity effects in black holes are generally expected to be unobservable if they set in at transplanckian curvature scales. Here, we challenge this expectation. A near-critical spin parameter can serve as a lever arm that translates Planckian quantum-gravity effects to a global change in the spacetime: the horizon dissolves and the black hole "lights up". We investigate this transition between a black hole and a horizonless spacetime and find that additional lensing features appear instantaneously, when the quantum-gravity effect is added. In the presence of an accretion disk, a second set of internal photon rings appears in addition to the exponentially stacked set of external photon rings. The internal and external photon rings merge into cresent-like features as a function of increasing spin parameter. We explore how these simulated images would be reconstructed by a radio-very-long-baseline-interferometry array like the Event Horizon Telescope. We find that a future next-generation Event Horizon Telescope may be sensitive to the additional lensing features.

... Since vacuum solutions to GR are Ricci flat, Kerr spacetime -just like Schwarzschild spacetime 1 Alternative axisymmetric black-hole branches need not be circular [47,48]. In fact, an application of the Janis-Newman complexification [49] -generalizing static and spherically symmetric solutions to axisymmetric and stationary candidate solutions -is known to only generate circular (and moreover algebraically special) spacetimes. While successfully generalizing Schwarzschild (Reissner-Nordström) spacetime to Kerr (Kerr-Newman) spacetime, all of which are circular and algebraically special [50], the Janis-Newman complexification will presumably fail in Quadratic Gravity. ...

We investigate the linear stability of the two known branches of spherically-symmetric black holes in Quadratic Gravity. We extend previous work on the long-wavelength (Gregory-Laflamme) instability of the Schwarzschild branch to a corresponding long-wavelength instability in the non-Schwarzschild branch. In both cases, the instability sets in below a critical horizon radius at which the two black-hole branches intersect. This suggests that classical perturbations enforce a lower bound on the horizon radius of spherically-symmetric black holes in Quadratic Gravity.

... Following newman janis algorithm [27], we have our metric to be, ...

In this paper we have took reissner nordstrom blackhole with cloud of strings and surrounds it with quintessence. we processed the metric through newman janis algorithm to get its rotating counterpart. the blackhole in study now is a roating charged blackhole with clouds of string surrounded by quintessence. we studied its nature of effective potential and unstable photon orbits. Finally we have plotted the blackhole shadow for various variable profiles.

... However, the Newman-Janis algorithm (NJA) introduced a revolutionary way to produce spinning spacetimes from a static, spherically symmetric seed metric without integrating any field equations (Newman & Janis 1965). Additionally, the revised NJA was used to obtain the first-ever rotating black hole solution in the loop quantum gravity (Brahma et al. 2021), and has been subsequently used to produce rotating black holes in modified gravities Boyer-Lindquist form, which is given as ) ...

A mathematically consistent rotating black hole model in Loop Quantum Gravity (LQG) is yet lacking. The scarcity of rotating black hole solutions in LQG substantially hampers the development of testing LQG from observations, e.g., from the Event Horizon Telescope (EHT) observations. The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87*. The EHT results are consistent with the shadow of a Kerr black hole of general relativity. We present LQG-motivated rotating black hole spacetimes (LMRBH), which are regular everywhere and asymptotically encompass the Kerr black hole as a particular case. LMRBH metric describes a multi-horizon black hole in the sense that it can admit up to three horizons, such that an extremal LMRBH, unlike Kerr black hole, refers to a black hole with angular momentum $a>M$. The metric, depending on the parameters, describes (1) black holes with only one horizon (BH-I), (2) black holes with an event and Cauchy horizons (BH-II), (3) black holes with three horizons (BH-III) or (4) no-horizon spacetime (NH) which, we show, is almost ruled out by the EHT observations. We constrain the LQG parameter with an aid of the EHT shadow observational results of M87* and Sgr A*,respectively, for an inclination angle of $17^0$ and $50^0$. In particular, the VLTI bound for the Sgr A*, $\delta\in (-0.17,0.01)$, constrains the parameters ($a,l$) such that for $0< l\leq 0.347851M\; (l\leq 2\times 10^6$ Km), the allowed range of $a$ is $(0,1.0307M)$. Together with EHT bounds of Sgr A$^*$ and M87$^*$ observables, our analysis concludes that the substantial part of BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. While EHT M87* results totally rules out the BH-III, but not that by Sgr A*.

... If there is an analytic solution to this equations, the rotation form of the corresponding space-time metric can be obtained. The content of the NJ method can be referred to the relevant literature (e.g., [40][41][42]). Follow the idea of this method, we will show the key derivation. ...

The successful observation of M87 supermassive black hole by the Black Hole Event Horizon Telescope(EHT) provides a very good opportunity to study the theory of gravity. In this work, we obtain the exact solution for the short hair black hole (BH) in the rotation situation, and calculate in detail how hairs affect the BH shadow. For the exact solution part, using the Newman-Janis algorithm, we generalize the spherically symmetric short-hair black hole metric to the rotation case (space-time lie element (2.25)). For the BH shadow part, we study two hairy BH models. In model 1, the properties of scalar hair are determined by the parameters $\alpha_{0}$ and $L$. In model 2, the scalar hair of the BH is short hair. In this model, the shape of the BH shadow is determined by scalar charge $Q_{m}$ and $k$. In general, various BH hairs have different effects on the shadows, such as non-monotonic properties and intersection phenomena mentioned in this work. Using these characteristics, it is possible to test the no-hair theorem in future EHT observations, so as to have a deeper understanding of the quantum effect of BHs. In future work, we will use numerical simulations to study the effects of various hairs on BHs and their observed properties.

... On the one hand, we want to explore the combined effect of rotation and electric charge parameters on the topological number of black holes, on the other hand, for the general consideration of the solution of four-dimensional black holes in the pure Einstein-Maxwell gravity theory, in this section, we turn to investigate the topological number of four-dimensional Kerr-Newman black hole [26,27], whose metric and Abelian gauge potential are ...

In this paper, we investigate the topological numbers for singly rotating Kerr black holes in arbitrary dimensions and four-dimensional Kerr-Newman black hole. We show that for uncharged black holes, the rotation parameter has a significant effect on the topological number, and for rotating black holes, the dimension of spacetime has a remarkable effect on the topological number too. Our current research provides more evidence that the conjecture put forward in [Phys. Rev. Lett. 129, 191101 (2022)], according to which all black hole solutions should be separated into three different topological classes, is accurate, at least in the pure Einstein-Maxwell gravity theory.

... The Newman−Janis algorithm (NJA) has been commonly used to generate rotating black hole solutions from their non-rotating or spherical counterparts [55]. While they developed this algorithm within general relativity, it has been more recently applied to non-rotating solutions in modified gravity theories [56][57][58][59]. ...

With a semiclassical polymerization in the loop quantum gravity (LQG), the interior of Schwarzschild black holes provides a captivating single-horizon regular black hole spacetime. The shortage of rotating black hole models in loop quantum gravity (LQG) substantially restrains the progress of testing LQG from observations. Motivated by this, starting with a spherical LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm, namely, the LQG-motivated rotating black holes (LMRBH), which encompasses Kerr ($l=0$) black holes as an exceptional case. We discover that for any random $l>0$, unlike Kerr black hole, an extremal LMRBH refers to a black hole with angular momentum $a>M$. The rotating metric, in parameter space, describes (1) black holes with an event and Cauchy horizons, (2) black holes with three horizons, (3) black holes with only one horizon or (4) no horizon spacetime. We also discuss the horizon and global structure of the LMRBH spacetimes and its dependence on $l/M$ that exhibits rich spacetime structures in the ($M,\;a,\;l$) parameter space.

... Back in 1975, Gürses and Gürsey established a basis how to construct a rotating counterpart of a spherically symmetric non-singular black hole with a regular center [34]. They derived a stationary and axisymmetric metric in the Boyer-Lindquist coordinates by the Newman-Janis complex transformation from a metric of the Kerr-Schild class [75][76][77]. The resulting Gürses-Gürsey metric (2.18) reduces to the Kerr spacetime when the mass function M (r) is constant [34]. ...

A bstract
We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well- known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

... Furthermore, Newman and Janis (NJ) found that one can obtain the Kerr metric by suitably complexifying the Schwarzschild solution in null polar coordinates and performing a shift [88]. Modern methods of amplitudes also allow us to comprehend the origin of the complex shift. ...

A bstract
We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.

... The closest one has to a pedagogical first-principles derivation of the Kerr spacetime is via the Newman-Janis trick [25,26], developed in 1965, which was immediately used in then deriving the electro-magnetically charged Kerr-Newman spacetime [27]. Despite many valiant efforts [28][29][30][31][32][33][34][35][36][37][38] it is still fair to say that no fully convincing explanation of why the Newman-Janis trick works has been forthcoming 1 . ...

Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr solution without signiﬁcant computational eﬀort. (Typically involving computer-aided symbolic algebra.) Perhaps the closest one gets in this regard is the Newman–Janis trick; a trick which requires several physically unmotivated choices in order to work. Herein we shall try to make some progress on this issue by using a non-ortho-normal tetrad based on oblate spheroidal coordinates to absorb as much of the messy angular dependence as possible, leaving one to deal with a relatively simple angle-independent tetrad-component metric. That is, we shall write g_{ab}= g_{AB} e^A_a e^B_b seeking to keep both the tetrad-component metric g_{AB} and the non-ortho-normal co-tetrad e^A_a relatively simple but non-trivial. We shall see that it is possible to put all the mass dependence into g_{AB}, while the non-ortho-normal co-tetrad e^A_a can be chosen to be a mass-independent representation of ﬂat Minkowski space in oblate spheroidal coordinates: (g_{Minkowski})_{ab} = η_{AB} e^A_a e^B_b. This procedure separates out, to the greatest extent possible, the mass dependence from the rotational dependence, and makes the Kerr solution perhaps a little less mysterious.

... There is a novel cross-check of the gauge theory results that one may perform. Although the electromagnetic multipole moments of the ffiffiffiffiffiffiffiffiffi Kerr p solution have not been previously calculated in the literature, one may instead consider a charged Kerr black hole, otherwise known as a Kerr-Newman black hole [67,68]. This is a solution of the Einstein-Maxwell equations, and as such consists of a metric plus a gauge field. ...

The classical double copy relates solutions of biadjoint, gauge, and gravity theories. The ultimate origin and scope of this correspondence remains mysterious, such that it is important to build a clear physical intuition of how the double copy operates. To this end, we consider the multipole expansion of exact classical solutions. Using a recently developed twistor translation of the classical double copy, we use well-established techniques to show that the multipole moments of arbitrary vacuum type-D gravity fields are exactly related to their counterparts in gauge and biadjoint scalar theories by the single and zeroth copies. We cross-check our results using previously obtained results for the Kerr metric and also provide new results for the “square root” of the Kerr-Taub-NUT solution.

... This confirms that the singularity and horizon in the toric Penrose diagrams are preserved under the diffeomorphism. The transformation is mathematically related to the so-called Newman-Janis (NJ) algorithm in Lorentzian signature [60]. However, it has crucial differences. ...

A bstract
The analytic continuation of the general signature (1, 3) Lorentzian Kerr-Taub-NUT black holes to signature (2, 2) Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter a . Remarkably, it is shown that the rotation a can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by (2, 2) three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically and enables a direct link to the S-matrix.

... In this paper, in order to obtain a non-circular shadow with distortions, we extend the above metric with m(r) given in Equation (3) to describe a rotating Kerr-like black hole. We employ the Newman-Janis algorithm [47][48][49][50][51][52][53] for a static, spherical regular black hole in Equation (1) and obtain a rotating regular black hole. For a spherical symmetric metric (Equation (1)), we introduce du = dt − dr/ f (r) to find the null coordinates {u, r, θ, φ}. ...

We investigate the shadows cast by a sort of new regular black hole which are characterized by an asymptotic Minkowski core and sub-Planckian curvature. First, we extend the metric with spherical symmetry to the one of rotating Kerr-like black holes and derive the null geodesics with a circular orbit near the horizon of the black hole. Then, we plot the shadows of black holes with different values for the deviation parameter. It is found that the size of the shadow shrinks with the increase in the deviation parameter, while the shape of the shadow becomes more deformed. In particular, by comparing with the shadow a Bardeen black hole and Hayward black hole with the same parameter values, we find that, in general, the shadows of black holes with Minkowski cores have larger deformations than those with de Sitter cores, which potentially provides a strategy to distinguish these two sorts of regular black holes with different cores by astronomical observation in the future.

... In order to discuss the connection between horizonless compact objects and regular black holes, we shall simplify the discussion by restricting our analysis to spherically symmetric solutions. While of course, rotating/axisymmetric solutions are those of most interest for astrophysical phenomenological studies, the considerations we are going to make herein are easily extendable to these more realistic configurations e.g. by suitably applying the Newman-Janis ansatz [40][41][42][43][44] to the solutions discussed in this work. In what follows, we shall see that for the standard cases of spherically symmetric regular black holes a unified description of the black hole and quasi-black hole limit is possible, with a one-to-one correspondence under suitable assumptions on the matter content of the spacetime. ...

We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner--Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt--Deser--Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that semiclassical physics contains the necessary ingredients to trigger the early stages of such dynamical evolution.

The recent opening of gravitational wave astronomy has shifted the debate about black hole mimickers from a purely theoretical arena to a phenomenological one. In this respect, missing a definitive quantum gravity theory, the possibility to have simple, meta-geometries describing in a compact way alternative phenomenologically viable scenarios is potentially very appealing. A recently proposed metric by Simpson and Visser is exactly an example of such meta-geometry describing, for different values of a single parameter, different non-rotating black hole mimickers. Here, we employ the Newman-Janis procedure to construct a rotating generalisation of such geometry. We obtain a stationary, axially symmetric metric that depends on mass, spin and an additional real parameter ℓ. According to the value of such parameter, the metric may represent a rotating traversable wormhole, a rotating regular black hole with one or two horizons, or three more limiting cases. By studying the internal and external rich structure of such solutions, we show that the obtained metric describes a family of interesting and simple regular geometries providing viable Kerr black hole mimickers for future phenomenological studies.

The lack of rotating black holes, typically found in nature, hinders testing modified gravity from astrophysical observations. We present the axially symmetric counterpart of an existing spherical hairy black hole in Horndeski gravity having additional deviation parameter Q, which encompasses the Kerr black hole as a particular case (Q=0). We investigate the effect of Horndeski parameter Q on the rotating black holes geometry and analytically deduce the gravitational deflection angle of light in the weak-field limit. For the S2 source star, the deflection angle for the Sgr A* model of rotating Horndeski gravity black hole for both prograde and retrograde photons is larger than the Kerr black hole values. We show how parameter Q could be constrained by the astrophysical implications of the lensing by this object. The thermodynamic quantities, Komar mass, and Komar angular momentum gets corrected by the parameter Q, but the Smarr relation Meff=2ST+2ΩJeff still holds at the event horizon.

We wish to carry forward to higher dimensions the insightful and novel method of obtaining the Kerr
metric proposed by one of us [Gen. Relativ. Gravit. 45, 2383 (2013)] for deriving the Myers-Perry rotating
black hole metric. We begin with a flat spacetime metric written in oblate spheroidal coordinates
(ellipsoidal geometry) appropriate for the inclusion of rotation, and then introduce arbitrary functions to
introduce a gravitational potential due to mass, which are then determined by requiring that a massless
particle experiences no acceleration, while a massive particle feels Newtonian acceleration at large $r$.
We further generalize the method to include the cosmological constant $\Lambda$ to obtain the Myers–Perry–
de Sitter/anti–de Sitter black hole metric.

We construct a new class of spherically symmetric black hole solutions in f(R)-gravity's rainbow¹ framework which is surrounded by string cloud configuration. In the thermodynamic analysis, we show that the black hole's temperature grows up for such small values of b parameter and also big values of it, graphically. In addition to the mass and charge of the black holes, we show that the presence of the rainbow function gr(ε) and cloud's strength b can also affect the size of the shadow. For the black hole solution, it is shown that the shadow size increases with the parameter b, but decreases with the parameter gr(ε). In addition, we have shown that the energy emission rate decreases with increase in gr(ε) and decrease in b parameter. We have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. The most important result derived from this study is that the height of this potential increases with decrease in gr(ε) parameter and increases in the coupling constant λ and the b parameter. We also investigate the impact of these parameters on the other thermodynamical quantities like temperature and heat capacity. There is a minimum on that between for one special value of b. From the temperature diagram versus the b parameter (T−b) and analogy with T−r+ diagrams, we can say that the b parameter behaves as the event horizon radius r+. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In d=5, the P-V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P-V diagrams. When d=6, the P-V diagrams are also more complex than that of the standard Van der Waals and we decompose them into two parts. One part behaves like the standard Van der Waals system. The other part is similar to the Schwarzschild-AdS black hole P-V diagrams where the isotherms turn and enter a region with negative pressures. The null geodesic equations are computed in d=5 spacetime dimensions by using the concept of symmetries and Hamilton-Jacobi equation and Carter separable method. With the null geodesics in hand, we then evaluate the celestial coordinates (x, y) and the radius Rs of the black hole shadow and represent it graphically.

Here we look at an application of the Hartle metric to describe a rotating version of the spherical string cloud/global monopole solution. While rotating versions of this solution have previously been constructed via the Newman-Janis algorithm, that process does not preserve the equation of state. The Hartle method allows for preservation of equation of state, at least in the sense of a slowly rotating perturbative solution. In addition to the direct utility of generating equations which could be used to model a region of a rotating string cloud or similar system, this work shows that it is possible to adapt the Hartle metric to slowly rotating anisotropic systems with Segre type [(11)(1,1)] following an equation of state between the distinct eigenvalues.

In this article, we considered the strong field approximation of nonlinear electrodynamics black hole and constructed its rotating counterpart by applying the modified Newman–Janis algorithm. The corresponding metric function in the strong field limit of the static black hole is identified in order to study the radius of photon sphere. However, the metric function for the rotating counterpart in the strong field limit is considered in order to study the horizon radius w.r.t spin parameter. We considered the Hamilton–Jacobi method to derive the geodesic equations for photon and constructed an orthonormal tetrad for deriving the equations for celestial coordinates in the observer’s sky. Shadows, distortions and energy emission rates are investigated and the results are compared for different values of nonlinear electrodynamics parameter, charge and spin. It is found that the presence of the nonlinear electrodynamics parameter affects the shape and size of the shadows and thus the distortion in the case of rotation. It is also found that the nonlinearity of electrodynamics diminishes the flatness in the shadow due to the effect of spin and other parameters.

With a semiclassical polymerization in the loop quantum gravity (LQG), the interior of the Schwarzschild black holes provides a captivating single-horizon regular black hole spacetime. The shortage of rotating black hole models in loop quantum gravity (LQG) substantially restrains the progress of testing LQG from observations. Motivated by this, starting with a spherical LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm, namely, the LQG-motivated rotating black holes (LMRBH), which encompasses Kerr ( l = 0) black holes as an exceptional case. We discover that for any random l > 0, unlike Kerr black hole, an extremal LMRBH refers to a black hole with angular momentum a > M . The rotating metric, in parameter space, describes (1) black holes with an event and Cauchy horizon, (2) black holes with three horizons, (3) black holes with only one horizon or (4) no horizon spacetime. We also discuss the horizon and global structure of the LMRBH spacetimes and its dependence on l / M that exhibits rich spacetime structures in the ( M, a, l ) parameter space.

In this article, we conduct a sequential study of possible observable images of black hole simulators described by two recently obtained rotating geometries in Einstein gravity, minimally coupled to a scalar field. One of them, “Kerr-like,” can be seen as a legitimate alternative to the rotating Fisher-Janis-Newman-Winicour solution, and the other (TSL) is a scalar generalization of the Tomimatsu-Sato-like solution. Unlike the previous version of the rotating Fisher-Janis-Newman-Winicour solution, these solutions do indeed satisfy the system’s equations of motion. Our study includes both analytical and numerical calculations of equatorial circular orbits, photon regions, gravitational shadows, and radiation from thin accretion disks for various values of the object’s angular momentum and scalar charge. The TSL solution was found to simulate Kerr for all valid parameter values with high accuracy. The maximum difference between the deviations of shadows from a circle for the Kerr and TSL cases does not exceed 1% and fits into the experimental observational data M87* and Sgr A*. However, near-extreme objects show two times smaller peak values of the observed outflow luminosity of the accretion disk than for the Kerr black hole. The Kerr-like solution cannot be ruled out by the experimental data for small values of the scalar charge either. As the scalar charge increases, the optical properties change dramatically. The shadow can become multiply connected, strongly oblate, and the photon region does not hide the singularity, so it should be classified as a strong singularity.

The purpose of this manuscript is to inspecting the phase transition as well as the critical phenomenon of charged quintessential Kerr–Newman-anti-de Sitter black hole with cloud of strings. In this regard, we evaluate the thermodynamic factors (Hawking temperature, angular momentum and entropy) in the framework of extended phase space. These factors fulfill the Smarr-Gibbs-Dehum equation in the existence of quintessence and cloud of strings. The critical behavior of thermodynamic factors is discussed via two techniques such as Maxwell equal-area law and Van-der Waal-like equation of state. It is obtained that the former one is more effective to observe the critical nature of the complex black holes. Further, we study the phase diagram in T−S plane using equal-area law and obtain an isobar depicting the coexistence era of two phases. It is concluded that black holes lower than the critical temperature exhibit the phase transition same as that of Van-der Waal fluid. At the end, we also analyze the influence of thermal variations on the black hole’s stability.

We present a new asymptotically flat black hole solution in Null Aether Theory (NAT) by applying Newman–Janis process. For this purpose, we study the asymptotically flat NAT black hole solution in Newman–Janis algorithm and then compute the tunneling radiation for NAT black hole. The Hawking temperature for NAT black hole depends upon the rotation parameter and charge of the black hole. The Hawking temperature describes a black hole with extremal event horizon. Furthermore, we analyze the graphical interpretation of Hawking temperature with respect to event horizon and check the stability of black hole under the influence of different parameters associated with black hole temperature.

We derive thermodynamic quantities such as the Hawking temperature, mass, entropy, heat capacity and study the thermodynamic phase transitions of rotating Bardeen black holes surrounded by quintessence-like matter. Interpreting the cosmological parameter as thermodynamic pressure and its conjugate variable as volume, the first law of black hole thermodynamics has been modified in the Anti-de Sitter (AdS) space. It then has been used to investigate the thermodynamics of the rotating Bardeen–AdS black hole with quintessence matter. Properties of the thermodynamic volume have also been analyzed through the study of compressibility and sound speed of the black hole. The black hole sound speed is associated with the adiabatic compressibility, and it equals the light speed for nonrotating black holes and decreases with increasing angular momentum. The nonrotating black holes are adiabatically incompressible, and as the angular momentum attains a maximum value in the extremal case, the compressibility grows maximum. We further derive the equation of state in the extended phase space and explore the critical behaviors of the black hole in the canonical ensemble. Graphs of phase transitions and critical behaviors show an accentuated influence of quintessence matter on the thermodynamic phase transitions and stability of the black holes and support the van der Waals-like phase transition behavior.

A bstract
We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

Quasi-periodic oscillations (QPOs), in particular, the ones with high frequencies, often observed in the power spectrum of black holes, are useful in understanding the nature of strong gravity since they are associated with the motion of matter in the vicinity of the black hole horizon. Interestingly, these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the most common ratio being 3:2. Several theoretical models are proposed in the literature which explain the HFQPOs in terms of the orbital and epicyclic frequencies of matter rotating around the central object. Since these frequencies are sensitive to the background spacetime, the observed HFQPOs can potentially extract useful information regarding the nature of the same. In this work, we investigate the role of regular black holes with a Minkowski core, which arise in gravity coupled to non-linear electrodynamics, in explaining the HFQPOs. Regular black holes are particularly interesting as they provide a possible resolution to the singularity problem in general relativity. We compare the model dependent QPO frequencies with the available observations of the quasi-periodic oscillations from black hole sources and perform a χ ² analysis. Our study reveals that most QPO models favor small but non-trivial values of the non-linear electrodynamics charge parameter. In particular, black holes with large values of non-linear electrodynamics charge parameter are generically disfavored by present observations related to QPOs.

Using the Mathisson–Papapetrou–Dixon equations together with the Tulczyjew spin-supplementary condition, we study the circular orbits of a spinning test particle moving in the equatorial plane of a quantum improved Rotating Black Hole (RBH) spacetime. This background metric incorporates a position-dependent gravitational constant [Formula: see text] and its behavior determines the quantum corrections to the properties of the Innermost Stable Circular Orbit (ISCO). The obtained results show that the radius of the event horizon as well as the radius of the ISCO for the quantum improved RBH are smaller than those of the Schwarzschild or Kerr solutions.

Starting from the leading soft term of the 5-point amplitude, involving a graviton and two Kerr black holes, that factorises into the product of the elastic amplitude without the graviton and the leading soft factor, we compute the infrared divergent contribution to the imaginary part of the two-loop eikonal. Then, using analyticity and crossing symmetry, we determine the radiative contribution to the real part of the two-loop eikonal and from it the radiative part of the deflection angle for spins aligned to the orbital angular momentum, the loss of angular momentum and the zero frequency limit of the energy spectrum for any spin and for any spin orientation. For spin one we find perfect agreement with recent results obtained with the supersymmetric worldline formalism.

We have studied the stability of wormhole geometries, under massless scalar, electromagnetic, and axial gravitational perturbations, in the context of higher dimensional spacetimes. Intriguingly, the construction of a wormhole spacetime in the presence of higher dimensions, known as braneworld wormholes, does not require the existence of exotic matter fields, unlike the scenario in four spacetime dimensions. Being a nonvacuum spacetime, the effective potential experienced by the axial gravitational perturbation differs considerably from the scenarios involving black holes. In particular, the present work provides one of the first attempts to study the gravitational perturbations of the wormhole spacetimes. Our analysis, involving both analytical and numerical techniques, demonstrates that there are echoes in the time domain signal of all the perturbations and the echo time delay is intimately related to the parameters originating from higher dimensions. Thereby combining the attempt to search for wormholes and extra dimensions, with the existence of gravitational wave echoes. Implications and future directions have also been discussed.

Algebraically special solutions of Einstein's empty-space field ; equations that are characterized by the existence of a geodesic and shear-free ; ray congruence are considered. A class of solutions is presented for which the ; congruence is diverging and is not necessarily hypersurface orthogonal. (C.E.S.);

The purpose of this paper is to propose a definition of multipole structure of gravitational sources in terms of the characteristic initial data for asymptotic solutions of the field equations. This definition is based upon a detailed study of the corresponding data for the linearized equations and upon the close analogy between the Maxwell and the linearized gravitational fields.