Properties of the distorted Kerr black hole

Abstract

We investigate the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources. The particular cases of quadrupole and octupole distortion are studied in detail. We also investigate the scalar curvature invariants of the horizon and compare their behaviour with the case of the isolated Kerr black hole. In a certain region of the parameter space the ergoregion consists of a compact region encompassing the horizon and a disconnected part extending to infinity. The curvature singularities in the domain of outer communication, when they exist, are always located on the boundary of the ergoregion. We present arguments that they do not lie on the compact ergosurface. For quadrupole distortion the compact ergoregion size is negatively correlated with the horizon angular momentum when the external sources are varied. For octupole distortion infinitely many ergoregion configurations can exist for a certain horizon angular momentum. For some special cases we can have J 2 /M 4 > 1 and yet avoid the naked singularity. * Alberta-Thy-14-15 † Internet address: abdolrah@ualberta.ca ‡ Internet address: jutta.kunz@uni-oldenburg.de § Internet address: pnedkova@phys.uni-sofia.bg ¶ Internet address: tzounis@ualberta.ca 1 arXiv:1509.01665v2 [gr-qc]

Many accelerating distorted black holes

“…However, the external gravitational field metric (2.11a) (and then (3.3a)) may be characterised by an unbounded growth of curvature invariants at spatial infinity, which corresponds to ρ 2 + z 2 → ∞ in Weyl coordinates. See [8] for a detailed study of possible curvature singularity in the domain of outer communication, for the distorted Kerr black hole. This feature is due to the presence of the sources that generate the external gravitational field, and the latter are thought to be located at large distances from the horizon.…”

“…The multipolar gravitational field is not a novel background for (single) black holes. First introduced by Doroshkevich, Zel'dovich and Novikov [4] in the '60s, these distorted black holes have been later studied by several authors including Chandrasekhar [5] and Geroch-Hartle [6] in the '80s, and several others in more recent times [7][8][9]. The novelty of our approach is the use of this background to remove conical singularities which usually stem superimposing more black sources.…”

Black hole shadows in fourth-order conformal Weyl gravity

“…Select approaches include analyzing the shadow characteristics of Kerr black holes with scalar hair [11], a five-dimensional Myers-Perry black hole [12], distorted Schwarzschild [13] and Kerr black holes [14], as well as the possibility of observing double images from a single black hole [15]. Additional shadow traits in other extensions and alternatives to general relativity include noncommutative gravity inspired black holes [16], Modified Gravity [17], f (r) gravity [18], a rotating Einstein-Born-Infeld black hole [19], regular black holes [20], and rotating non-singular black holes [21].…”

“…As illustrative examples, the Einstein-Born-Infeld shadow considered in [19] was found to be smaller than that of a Reissner-Nordström black hole. Other models such as the Kerr black hole with scalar hair predict shadows of distinguishable shape from those in general relativity [14]. Differentiability of shadow characteristic by the EHT between Randall-Sundrum and Einstein-Gauss-Bonnet black holes have also been considered [8].…”

Cosmological isotropic matter–energy generalizations of Schwarzschild and Kerr metrics

“…Vaidya [12] has also given a very general form of the Kerr-Schild metric satisfying the Einstein's field equations. Tzounis et al, [13] explored the properties of the ergoregion and the location of the curvature singularities for the Kerr black hole distorted by the gravitational field of external sources and they also studied the scalar curvature invariants of the horizon and compared their behaviour with the case of the isolated Kerr black hole. Lake et al, [14] examined the global structure of the family of Kerr-de Sitter spacetimes.…”