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We analyze the post-Newtonian orbit of stars around a deformed Kerr black hole. The deformation we consider is a class of disformal transformations of a nontrivial Kerr solution in scalar-tensor theory which are labeled via the disformal parameter $D$. We study different limits of the disformal parameter, and compare the trajectories of stars orbiting a black hole to the case of the Kerr spacetime in general relativity, up to 2PN order. Our findings show that for generic nonzero $D$, the no-hair theorem of general relativity is violated, in the sense that the black holes quadrupole $Q$ is not determined by its mass $M$ and angular momentum $J$ through the relation $Q=-J^2/M$. Limiting values of $D$ provide examples of simple and exact noncircular metric solutions, whereas in a particular limit, where $1+D$ is small but finite, we obtain a leading correction to the Schwarzschild precession due to disformality. In this case, the disformal parameter is constrained using the recent measurement of the pericenter precession of the star S2 by the GRAVITY Collaboration.
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If a lot of dark matter particles accumulate near the black hole, then the chances of detecting dark matter signals near a black hole are greatly increased. These effects may be observed by the Event Horizon Telescope (EHT), Tianqin project, Taiji project, Laser Interferometer Space Antenna (LISA) and Laser Interferometer Gravitational-Wave Observatory (LIGO). In this work, we explore the effects of dark matter spikes on black hole space-time. For the Schwarzschild-like black hole case, we consider Newton$$s approximation and perturbation approximation. This makes it possible to use Xu$$s method to solve the Einstein field equation, and extend Schwarzschild-like black hole to Kerr-like black hole (BH) via Newman-Janis (NJ) algorithm. By analyzing the dark matter spike on the black hole event horizon (EH), stationary limit surfaces (SLS), ergosphere and energy-momentum tensors (EMT), we found that compared with the dark matter halo, the dark matter spike would have a higher effect on the black hole by several orders of magnitude. Therefore, if there is a dark matter spike near the black hole, it is very possible to test the dark matter model through gravitational wave (GW) observation and EHT observation.
It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the Planck-mass. Usually this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum-length most readily leads to the idea of the black hole remnants, here we examine the behaviour of the potential that follows from the Planck-length deformed QFT in absence of the minimum length and show that it might also lead to the formation of the Planck mass black holes in some particular cases. The calculations are made for higher-dimensional case as well. Such black hole remnants might be considered as a possible candidates for the dark-matter.
Ongoing observations in the strong-field regime are in optimal agreement with general relativity, although current errors still leave room for small deviations from Einsteins theory. Here we summarise our recent results on superradiance of scalar and electromagnetic test fields in Kerr-like spacetimes, focusing mainly on the Konoplya--Zhidenko metric. We observe that, while for large deformations with respect to the Kerr case superradiance is suppressed, it can be nonetheless enhanced for small deformations. We also study the superradiant instability caused by massive scalar fields, and we provide a first estimate of the effect of the deformation on the instability timescale.
We obtain the shadow cast induced by the rotating black hole with an anisotropic matter. A Killing tensor representing the hidden symmetry is derived explicitly. The existence of separability structure implies a complete integrability of the geodesic motion. We analyze an effective potential around the unstable circular photon orbits to show that one side of the black hole is brighter than the other side. Further, it is shown that the inclusion of the anisotropic matter ($Kr^{2(1-w)}$) has an effect on the observables of the shadow cast. The shadow observables include approximate shadow radius $R_s$, distortion parameter $delta_s$, area of the shadow $A_s$, and oblateness $D_{os}$.
Quasinormal modes of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the intriguing features of these modes is that they respect the no-hair theorem, and hence, they can be used to test black hole space-times and the underlying gravitational theory. In this paper, we exhibit three different aspects of how black hole quasinormal modes could be altered in theories beyond Einstein general relativity. These aspects are the direct alterations of quasinormal modes spectra as compared with those in general relativity, the violation of the geometric correspondence between the high-frequency quasinormal modes and the photon geodesics around the black hole, and the breaking of the isospectrality between the axial and polar gravitational perturbations. Several examples will be provided in each individual case. The prospects and possible challenges associated with future observations will be also discussed.
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