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Recently, simple metrics of spherically symmetric black hole in dark matter halo were obtained by Xu et al, and extended to the case of rotation. Based on these two metrics of spherically symmetric black hole, we study the echo signals of CDM and SFDM models in scalar and electromagnetic fields, and make comparisons with the Schwarzschild black hole. Our results show that the black hole echoes in dark matter halo are different from the Schwarzschild black hole, hence the signals of echo can be used to distinguish different dark matter models. The echo signals appear after the first exponential decay, and decrease with increasing parameter $l$. The values of echo of CDM are approximately between $10^{-1}$ and $10^{-5}$, that of SFDM are between $10^{-2}$ and $10^{-6}$; The values of classic black hole are approximately between $10^{-4}$ and $10^{-8}$. The overall echoes of CDM are stronger than that of SFDM in the same condition, which is easier to be detected. In addition, the values of echo frequency using the six-order WKB method and Prony method are in good agreement.
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For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetric black hole solutions in dark matter halo. Utilizing Newman-Jains method, we further generalize spherical symmetric black holes to rotational black holes. As examples, we obtain the space-time metric of black holes surrounded by Cold Dark Matter and Scalar Field Dark Matter halos, respectively. Our main results regarding the interaction between black hole and dark matter halo are as follows: (i) For both dark matter models, the density profile always produces cusp phenomenon in small scale in the relativity situation; (ii) Dark matter halo makes the black hole horizon to increase but the ergosphere to decrease, while the magnitude is small; (iii) Dark matter does not change the singularity of black holes. These results are useful to study the interaction of black hole and dark matter halo in stationary situation. Particularly, the cusp produced in the $0sim 1$ kpc scale would be observable in the Milky Way. Perspectives on future work regarding the applications of our results in astrophysics are also briefly discussed.
We consider a very simple model for gravitational wave echoes from black hole merger ringdowns which may arise from local Lorentz symmetry violations that modify graviton dispersion relations. If the corrections are sufficiently soft so they do not remove the horizon, the reflection of the infalling waves which trigger the echoes is very weak. As an example, we look at the dispersion relation of a test scalar field corrected by roton-like operators depending only on spatial momenta, in Gullstrand-Painleve coordinates. The near-horizon regions of a black hole do become reflective, but only very weakly. The resulting ``bounces of infalling waves can yield repetitive gravity wave emissions but their power is very small. This implies that to see any echoes from black holes we really need an egregious departure from either standard GR or effective field theory, or both. One possibility to realize such strong echoes is the recently proposed classical firewalls which replace black hole horizons with material shells surrounding timelike singularities.
It has been shown that the nonthermal spectrum of Hawking radiation will lead to information-carrying correlations between emitted particles in the radiation. The mutual information carried by such correlations can not be locally observed and hence is dark. With dark information, the black hole information is conserved. In this paper, we look for the spherically symmetric black hole solution in the background of dark matter in mimetic gravity and investigate the radiation spectrum and dark information of the black hole. The black hole has a similar spacetime structure to the Schwarzschild case, while its horizon radius is decreased by the dark matter. By using the statistical mechanical method, the nonthermal radiation spectrum is calculated. This radiation spectrum is very different from the Schwarzschild case at its last stage because of the effect of the dark matter. The mimetic dark matter reduces the lifetime of the black hole but increases the dark information of the Hawking radiation.
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.
We show that a black hole surrounded by scalar dark matter develops scalar hair. This is the generalization of a phenomenon pointed out by Jacobson, that a minimally coupled scalar with a non-trivial time dependence far away from the black hole would endow the black hole with hair. In our case, the time dependence arises from the oscillation of a scalar field with a non-zero mass. We systematically explore the scalar profile around the black hole for different scalar masses. In the small mass limit, the scalar field has a $1/r$ component at large radius $r$, consistent with Jacobsons result. In the large mass limit (with the Compton wavelength of order of the horizon or smaller), the scalar field has a $1/r^{3/4}$ profile yielding a pile-up close to the horizon, while distinctive nodes occur for intermediate masses. Thus, the dark matter profile around a black hole, while challenging to measure, contains information about the dark matter particle mass. As an application, we consider the case of the supermassive black hole at the center of M87, recently imaged by the Event Horizon Telescope. Its horizon size is roughly the Compton wavelength of a scalar particle of mass $10^{-20}$ eV. We consider the implications of the expected scalar pile-up close to the horizon, for fuzzy dark matter at a mass of $10^{-20}$ eV or below.
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