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Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
Abstract
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 Kerr-Newman metric is an exact solution of the Einstein-Maxwell equation, which describes stationary spacetime with the angular momentum and the electric charge. In 1963, Kerr first found the metric of a spinning object in a gravitational field [17], which is a generalization of the Schwarzschild metric. Two years later, Newman et al. obtained the metric that can describe both rotating and charged spacetime [18]. ...
... This can be used to constrain physical quantities of the black hole in a cavity. We turn to consider the three equations mentioned above: the horizon radius determined by ∆ = 0 in Eq. (17), the angular momentum J = M a and the entropy in Eq. (27). Solving these equations yields ...
The quasi-local energy of a Kerr-Newman black hole in a finite spherical cavity with fixed radius is derived from the Hamiltonian, and the first law of thermodynamics is constructed accordingly. In a canonical ensemble, the black hole could undergo a van der Waals-like phase transition. The temperature where the phase transition occurs decreases with the increase of the angular momentum or the charge. Our results imply that the thermodynamics of a Kerr-Newman black hole in a cavity shows extensive similarities to the one in AdS spacetime.
... Theory-agnostic metrics can often be written down in a relatively convenient form, but do not have a physical theory behind them and can be difficult to interpret. They can, however, be used without reservation for null tests of GR, where parametrized deviations from the BH solutions of GR (often the rotating one known as the Kerr solution [25]) provide a handle on violations of GR via the no-hair theorem. ...
Black hole based tests of general relativity have proliferated in recent times with new and improved detectors and telescopes. Modelling of the black hole neighborhood, where most of the radiation carrying strong-field signature originates, is of utmost importance for robust and accurate constraints on possible violations of general relativity. As a first step, this paper presents the extension of general relativistic magnetohydrodynamic simulations of thin accretion disks to parametrically deformed black holes that generalize the Kerr solution. The extension is based on \textsc{harmpi}, a publicly available member of the \textsc{harm} family of codes, and uses a phenomenological metric to study parametric deviations away from Kerr. The extended model is used to study the disk structure, stability, and radiative efficiency. We also compute the Fe K$\alpha$ profiles in simplified scenarios and present an outlook for the future.
... When a bosonic wave is impinging upon a rotating black hole, the wave reflected by the event horizon will be amplified if the wave frequency ω lies in the following superradiant regime [7,9,13,15,16] ...
In this article, it mainly discusses that the first-order phase transition (Davis transition) is isomorphic, and there is a potential barrier outside the superradiative event horizon, and the thermodynamic geometry second-order phase transition (R geometric curvature scalar divergence) is isomorphic, and there is a potential barrier(instability). This brings about a new method to find the superradiative stability. When there is an interval between the divergence point of the Davis phase transition and the divergence point of the R geometric curvature scalar, that interval is the superradiative stability condition of the black hole.
The motion of an object under the influence of force fields and/or media is described by means of a world-line with least action in its influenced spacetime. For any spacetime point x and a four-vector u, measured in the frame of an inertial observer, a unifying and physically meaningful action function L(x, u) generating the action is defined. To ensure independence of the observer and of the parametrization on the world-line, L(x, u) must be Lorentz invariant and positive homogeneous of order 1 in u. The simplest such L(x, u) depends on two four-potentials. In most cases, these potentials can be defined directly from the sources of the fields without the need for field equations. The unified dynamics equation resulting from this action, properly describes the motion in any electromagnetic field, in any static gravitational field, in a combined electromagnetic and gravitational field, as well as the propagation of light and charges in isotropic media.
We study the tidal forces and their effect in
Schwarzschild black hole surrounded with clouds of strings
and quintessence. Two horizons are present for this black
hole and the event horizon shrinks on increasing the values
of both, the string cloud and quintessence parameters. Tidal
forces in radial as well as angular directions are independent
of string cloud parameter a.Geodesic deviation equations are
devised and solved for this BH metric. For numerical representation
of the solutions of geodesic deviation equations
two different initial conditions have been applied. Results
are compared with that of Schwarzschild black hole metric.
We consider a pseudoscalar axion-like field coupled to a Chern-Simons gravitational anomaly term. The axion field backreacts on a rotating Kerr black hole background, resulting in modifications in the spacetime. In an attempt to determine potentially observable signatures, we study the angular momentum of the system of the modified Kerr-like black hole and the axionic matter outside the horizon of the black hole. As the strength of the coupling of the axion field to the Chern-Simons term is increasing, the requirement that the total angular momentum of the system remain constant forces the black hole angular momentum to decrease. There exists a critical value of this coupling beyond which the black hole starts to rotate in the opposite direction, with an increasing magnitude of its angular momentum. We interpret this effect as a consequence of the exchange of energy between the axionic matter and the gravitational anomaly, which is sourced by the rotating black hole.
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.
Closed Timelike Curves (CTCs) were introduced both in Special Relativity and the classical General Relativity. Due to CTC’s high confluence with time and causality, some discussions related to causality principle, determinism, arrow of time, philosophy of time and some approaches from physicists and scientists about Time were made. By defining physical time, the relation between time and other physical phenomena were discussed and we extensively introduced the Conformal Geometry and explained how conformal diagrams (Penrose diagrams) are constructed for various spacetimes. Then we took a more detailed look at CTCs. In the first place, by introducing some of the most notable spacetimes including CTCs, their characteristics and deficiencies were discussed. After all, we succeeded on guessing CTCs in Minkowski and Schwarzschild spacetimes, in two spacelike and timelike schemes, and noted the effect of topology on the existence of closed timelike paths in these space-times.
Einstein's equations for empty space are solved for the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves. Some of these metrics may be considered as representing a simple kind of spherical, outgoing radiation. (Among them are solutions admitting no Killing field whatsoever.) Examples of solutions to the Maxwell-Einstein equations with a similar geometry are also given.