Davide Batic

Khalifa University | KU · Mathematics

In this paper, we undertake a comprehensive examination of quasinormal modes linked to Lee-Wick black holes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Such black holes can display a rich structure of horizons, and our analysis considers all the representative scenarios, including extremal and n...

In this paper, we undertake a comprehensive examination of quasinormal modes (QNMs) linked to Morris-Thorne, also known as Bronnikov-Ellis wormholes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Our research corrects inaccuracies previously reported in the literature and addresses areas where the...

In this paper, we undertake a comprehensive examination of quasinormal modes (QNMs) linked to Morris–Thorne, also known as Bronnikov–Ellis wormholes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Our research corrects inaccuracies previously reported in the literature and addresses areas where the...

The recent fit of cosmological parameters by the Dark Energy Spectroscopic Instrument (DESI) collaboration will have a significant impact on our understanding of the universe. Given its importance, we conduct several consistency checks and draw conclusions from the fit. Specifically, we focus on the following key issues relevant to cosmology: (i) t...

We set up the Wheeler-DeWitt (WDW) equation for late gravitational collapse. The fact that the gravitational collapse and the expanding/ collapsing universe can be described within the realm of the Robertson-Walker metric renders the corresponding WDW equation for collapsing matter a timeless Schr\"odinger equation. We explore the consequences of s...

Among the recent extensions to standard General Relativity, $f(R,\mathcal{L}_m)$ gravity has risen an interest given the possibility of coupling between geometry and matter. We examine the simplest model with non-minimal coupling in the context of cosmology. We pay special attention to the question of how far this model could reproduce the observat...

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous cl...

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous cl...

Among the recent extensions to standard General Relativity, f ( R , L m ) gravity has risen an interest given the possibility of coupling between geometry and matter. We examine the simplest model with non-minimal coupling in the context of cosmology. We pay special attention to the question of how far this model could reproduce the observational f...

In this work, we join the controversial discussion on singular and nonsingular black holes using the Gaussian distribution. Our result which uses correct boundary conditions shifts the debate in favor of regular black holes at the center. The present findings add new insights into the ongoing discussions surrounding singularities in black hole solu...

In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our results further reinforce the importance and special character of axisymmetric solutions in general relativity and...

We show how the Gambier equation arises in connection to Friedmann-Lema$\mbox{\^{i}}$tre-Robertson-Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlev$\acute{\mbox{e}}$ property in $2+1$ dimensions. We also consider spec...

In this paper, we show how the Gambier equation arises in connection to Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlevé property in (2 + 1) dimensions. We also consider special cases of...

Scalar, vector and tensor conserved quantities are essential tools in solving different problems in physics and complex, nonlinear differential equations in mathematics. In many guises they enter our understanding of nature: charge, lepton, baryon numbers conservation accompanied with constant energy, linear or angular total momenta and the conserv...

Scalar, vector and tensor conserved quantities are essential tools in solving different problems in physics and complex, nonlinear differential equations in mathematics. In many guises they enter our understanding of nature: charge, lepton, baryon numbers conservation accompanied with constant energy, linear or angular total momenta and the conserv...

We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the approximants. With the help of this alternative termination condition and certain properties of continuous fractions,...

We introduce a new approach to the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique, and we develop a novel termination condition in terms of the approximants. With the help of this alternative termination condition and certain properties of continuous fractions, we...

In this work, we derive exact analytic formulae for the inner and outer surfaces representing the boundary of the ergoregion appearing in the Tomimatsu–Sato (TS) metric. Exact expressions for the radii of the ergoregion in prolate spheroidal coordinates and in Boyer-Lindquist coordinates are obtained. We also found that in addition to the ring-shap...

Dark Matter (DM) is usually studied in connection with rotational curves in the outskirts of the galaxies. However, the role of DM might be different in the galactic bulges and centers where Supermassive Black Holes (SMBHs) dominate the gravitational interaction. Indeed, given the fact that DM is the dominant matter species in the Universe, it is n...

Dark Matter (DM) is usually studied in connection with rotational curves in the outskirts of the galaxies. However, the role of DM might be different in the galactic bulges and centers where Supermassive Black Holes (SMBHs) dominate the gravitational interaction. Indeed, given the fact that DM is the dominant matter species in the Universe, it is n...

In view of a result recently published in the context of deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated to the angular equation arising after the separation of the Dirac equation in the Kerr metric and we show how efficiently a quasi-linear first order PDE for the angular eigenvalues can be derived...

In view of a result recently published in the context of the deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated with the angular equation arising after the separation of the Dirac equation in the Kerr metric, and we show how a quasilinear first order PDE for the angular eigenvalues can be derived effic...

We reconsider the case of the geodesic motion of a massive and massless beam of test particles in a gravitational wave. In particular, we use a direct Lagrangian approach which simplifies the calculation. Our findings differ partly from previously performed calculations The final result can be interpreted as rings of light seen by the observer. We...

We reconsider the case of the geodesic motion of a massive and massless beam of test particles in a gravitational wave. In particular, we use a direct Lagrangian approach which simplifies the calculation. Our findings differ partly from previously performed calculations The final result can be interpreted as rings of light seen by the observer. We...

We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein's equations with and without spherical symmetry. A general formula for the deflection angle in the weak lensing regime for the Schwarzschild-Tangherlini (ST) metric is derived. In addition,...

We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein’s equations with and without spherical symmetry. A general formula for the deflection angle in the weak lensing regime for the Schwarzschild-Tangherlini (ST) metric is derived. In addition,...

The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections a...

In this work, we study the weak and strong gravitational lensing in the presence of an accelerating black hole in a universe with positive cosmological constant $\Lambda$. First of all, we derive new perturbative formulae for the event and cosmological horizons in terms of the Schwarzschild, cosmological and acceleration scales. In agreement with p...

In this work, we study the weak and strong gravitational lensing in the presence of an accelerating black hole in a universe with a positive cosmological constant Λ. First of all we derive new perturbative formulas for the event and cosmological horizons in terms of the Schwarzschild, cosmological and acceleration scales. In agreement with previous...

The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections a...

We consider the possibility of having Dark Matter (DM) black holes motivated by the Einasto density profile. This generalizes both the noncommutative mini black hole model and allows DM to enter as the matter constituent which makes up the black hole. We show that it is possible to construct a black hole solution for each value of the Einasto index...

We consider the possibility of having Dark Matter (DM) black holes motivated by the Einasto density profile. This generalizes both the noncommutative mini black hole model and allows DM to enter as the matter constituent which makes up the black hole. We show that it is possible to construct a black hole solution for each value of the Einasto index...

We discuss the propagation of light in the C-metric. We discover that null geodesics admit circular orbits only for a certain family of orbital cones. Explicit analytic formulae are derived for the orbital radius and the corresponding opening angle fixing the cone. Furthermore, we prove that these orbits based on a saddle point in the effective pot...

We consider the non-linear classical field theory which results from adding to the Maxwell's Lagrangian the contributions from the weak-field Euler-Heisenberg Lagrangian and a non-uniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the...

We consider the nonlinear classical field theory which results from adding to the Maxwell’s Lagrangian the contributions from the weak-field Euler–Heisenberg Lagrangian and a nonuniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the m...

We discuss the propagation of light in the C-metric. We discover that null geodesics admit circular orbits only for a certain family of orbital cones. Explicit analytic formulae are derived for the orbital radius and the corresponding opening angle fixing the cone. Furthermore, we prove that these orbits based on a saddle point in the effective pot...

We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of classical mechanics, particularly the absence of an uncertainty principle between the position and momentum of...

We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of classical mechanics, particularly the absence of an uncertainty principle between the position and momentum of...

We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk vi...

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel-Kramers-Brillouin (WKB) approximation we show that the widely used WKB method does not conv...

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel–Kramers–Brillouin (WKB) approximation we show that the widely used WKB method does not conv...

We address the concerns raised by the author of "Comment: Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime" appeared in arXiv:1807.05940. In particular, we explain why the analysis in our paper [Phys. Rev. D{\bf{98}}, 024017 (2018)] is relevant and correct.

We explain why the analysis in our paper [Phys. Rev. D 98, 024017 (2018)] is relevant and correct.

We probe into universes filled with Quark Gluon Plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the Quark Gluon Plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk vi...

Cosmologies based on General Relativity encompassing an anti-symmetric connection (torsion) can display nice desirable features as the absence of the initial singularity and the possibility of inflation in the early stage of the universe. After briefly reviewing the standard approach to the cosmology with torsion, we generalize it to demonstrate th...

Cosmologies based on General Relativity encompassing an anti-symmetric connection (torsion) can display nice desirable features as the absence of the initial singularity and the possibility of inflation in the early stage of the universe. After briefly reviewing the standard approach to the cosmology with torsion, we generalize it to demonstrate th...

We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general homogeneous linear ordinary differential equation allow to construct several new indefinite integrals for the confluent...

We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general homogeneous linear ordinary differential equation allow to construct several new indefinite integrals for the confluent...

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also derive new indefinite integrals involving the Gauss hypergeometric function and products of hypergeometric functio...

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also derive new indefinite integrals involving the Gauss hypergeometric function and products of hypergeometric functio...

We show that not all quasinormal modes of a massless scalar field in the Schwarzschild metric are encoded in the corresponding characteristic equation expressed by means of a continued fraction. We provide an analytical formula for these new hitherto missing quasinormal modes, and in doing that we also construct a generalization of the Gauss conver...

We show that not all quasinormal modes of a massless scalar field in the Schwarzschild metric are encoded in the corresponding characteristic equation expressed by means of a continued fraction. We provide an analytical formula for these new hitherto missing quasinormal modes, and in doing that we also construct a generalization of the Gauss conver...

Получены наиболее общие семейства дифференциальных операторов первого и второго порядков, почти коммутирующих с дифференциальными операторами класса Гойна. Среди полученных семейств выделены те, которые коммутируют с классом Гойна. В частности, обнаружено, что некоторое обобщенное уравнение Гойна коммутирует с дифференциальным оператором Гойна, что...

Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an $\hbar$-correction to the $g_{00}$ component of the Schwarzschild metric, we construct a quantum mechanically corrected metric assuming $-g_{00}=g^{rr}$. We show how the Bekenstein black hole entropy $S$ receives its logarithmic contribution prov...

We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In particular, we discover that a certain generalized Heun equation commutes with the Heun differential operator...

We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In particular, we discover that a certain generalized Heun equation commutes with the Heun differential operator...

We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which have been claimed for the case when the energy is less than the particle's mass. We explicitly prove t...

We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which have been claimed for the case when the energy is less than the particle's mass. We explicitly prove t...

The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of “projections” onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimension...

It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior o...

It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior o...

Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an $\hbar$-correction to the $g_{00}$ component of the Schwarzschild metric, we construct a quantum mechanically corrected metric assuming $-g_{00}=g^{rr}$. We show how the Bekenstein black hole entropy $S$ receives its logarithmic contribution prov...

We consider a fermion in the presence of a rotating black hole immersed in a universe with positive cosmological constant. After deriving new formulae for the event, Cauchy and cosmological horizons we adopt the Carter tetrad to separate the aforementioned equation into a radial and angular equation. We show how the Chandrasekhar ansatz leads to th...

Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the Schr\"odinger equations can be transformed into another well-known equation for transcendental function (e.g....

We consider the motion of light on different spacetime manifolds by calculating the deflection angle, lensing properties and by probing into the possibility of bound states. The metrics in which we examine the light motion include, among other, a general relativistic Dark Matter metric, a dirty Black Hole and a Worm Hole metric, the last two inspir...

We present the extension of the Einstein-Maxwell system called electrovac universes by introducing a cosmological constant $\Lambda$. In the absence of the $\Lambda$ term, the crucial equation in solving the Einstein-Maxwell system is the Laplace equation. The cosmological constant modifies this equation to become in a non-linear partial differenti...

The present article discusses the two point connection problem for Heun's differential equation. We employ a contour integral method to derive connection matrices for a sub-class of the Heun equation containing 3 free parameters. Explicit expressions for the connection coefficients are found.

We review different methods of generating potentials such that the one-dimensional Schr\"{o}dinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transform...

Rainbow, glory and orbiting scattering are usually described by the properties of the classical deflection function related to the real part of the quantum mechanical scattering phase shift or by the diffractive pattern of the quantum mechanical cross sections. Here we show that the case of orbiting scattering of massless spin 0, 1 and 2 particles...

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstr\"{o}m and Reissner-Nordstr\"{o}m-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born app...

It is shown here that the extraction of quasinormal modes (QNMs) within the first Born approximation of the scattering amplitude is mathematically not well founded. Indeed, the constraints on the existence of the scattering amplitude integral lead to inequalities for the imaginary parts of the QNM frequencies. For instance, in the Schwarzschild cas...

We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Sc...

We use the Dirac equation coupled to a background metric to examine what happens to quantum-mechanical observables like the probability density and the radial current in the vicinity of a naked singularity of the Reissner–Nordström type. We find that the wave function of the Dirac particle is regular in the point of the singularity. We show that th...

One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of effects of noncommutativity, this effect is in particular important, as it removes the poin...

We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE. Keywordsquantum field theory i...

We derive a transformation of the noncommutative geometry inspired Schwarzschild solution into new coordinates such that the apparent unphysical singularities of the metric are removed. Moreover, we give the maximal singularity-free atlas for the manifold with the metric under consideration. This atlas reveals many new features e.g. it turns out to...

We study the stability of the noncommutative Schwarzschild black hole interior by analysing the propagation of a massless scalar field between the two horizons. We show that the spacetime fuzziness triggered by the field higher momenta can cure the classical exponential blue-shift divergence, suppressing the emergence of infinite energy density in...

We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the noncommutative geometry. In the framework of the noncommutative geometry, this solution is interpreted as a mini black hole which has the Schwarzschild geometry outside the event horizon, but whose standard central singularity is repl...

In this paper we compute the square root of the generalized squared total angular momentum operator $J$ for a Dirac particle in the Kerr-Newman metric. The separation constant $\lambda$ arising from the Chandrasekahr separation ansatz turns out to be the eigenvalue of $J$. After proving that $J$ is a symmetry operator, we show the completeness of C...

In this paper we compute the square root of the generalized squared total angular momentum operator J for a Dirac particle in the Kerr-Newman metric. The separation constant [lambda] arising from the Chandrasekahr separation ansatz turns out to be the eigenvalue of J. After proving that J is a symmetry operator, we show the completeness of Chandras...

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. For this purpose a self-adjoint holomorphic operator family associated with this eigenvalue problem is considered. We show that the eigenvalues satisfy a first-order nonlinear differential equation with respect to the blac...

We study two different ways to analyze the Hawking evaporation of a Schwarzschild-de Sitter black hole. The first one uses the standard approach of surface gravity evaluated at the possible horizons. The second method derives its results via the Generalized Uncertainty Principle (GUP) which offers a yet different method to look at the problem. In t...

In this article we show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of Quantum Field Theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. To this purpose a self-adjoint holomorphic operator family associated to this eigenvalue problem is considered. We show that the eigenvalues satisfy a first order nonlinear differential equation with respect to the black h...

Starting with the Dirac equation in the extreme Kerr metric we derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the class of smooth compactly supported functions.

Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spin $s=\pm 2$ (gravitational waves), $s=\pm 1$ (electromagnetic waves) and $s=\pm 1/2$ (neutrinos) is an Heun equation in disguise.

In this paper we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of quantum field theory in curved spacetimes. In particular, we relate the separated radial part of a massive Dirac equation in the Kerr–Newman metric to the static perturbations for the non-extremal Reissner–Nordström solution to a GHE.

Starting with the Dirac equation outside the event horizon of a nonextreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is done by implementing a time-dependent logarithmic phase shift from the free dynamics to offset the long range te...

In this article we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of Quantum Field Theory in curved space-times. In particular, we relate the separated radial part of a massive Dirac equation in the Kerr-Newman metric and the static perturbations for the non-extremal Reissner-Nordstr\"{o}m solution to...

We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use to derive an integral representation for the propagator of solutions of the Cauchy problem with initial data...

In this paper we study for a given azimuthal quantum number $\kappa$ the eigenvalues of the Chandrasekhar-Page angular equation with respect to the parameters $\mu:=am$ and $\nu:=a\omega$, where $a$ is the angular momentum per unit mass of a black hole, $m$ is the rest mass of the Dirac particle and $\omega$ is the energy of the particle (as measur...