The presence of dark matter around a black hole remarkably affects its spacetime. We consider the effects of dark matter on the shadow of a new solution to the Einstein equations that describes a rotating black hole in the background of perfect dark matter fluid (PFDM), along with its extension to nonzero cosmological constant Λ. Working in Boyer-Lindquist coordinates, we consider the effects of the PFDM parameter α on the shadow cast by a black hole with respect to an observer at position (ro, θo). By applying the Gauss-Bonnet theorem to the optical geometry we find that notable distortions from a Kerr black hole can occur. We describe their dependence on α and Λ.

In this paper we present a new black hole solution surrounded by dark matter halo in the galactic center using the mass model of M87 and that coming from the Universal Rotation Curve (URC) dark matter profile representing family of spiral galaxies. In both cases the DM halo density is cored with a size r 0 and a central density ρ 0 : ρ(r) = ρ 0 /(1 + r/r 0 )(1 + (r/r 0 ) 2 ). Since r 0 ρ 0 = 120 M /pc 2 [5], then by varying the central density one can reproduce the DM profile in any spiral. Using the Newman-Jains method we extend our solution to obtain a rotating black hole surrounded by dark matter halo. We find that, the apparent shape of the shadow beside the black hole spin a, it also depends on the central density of the surrounded dark matter ρ 0 . As a specific example we consider the galaxy M87, with a central density ρ 0 = 6.9 × 10 6 M /kpc 3 and a core radius r 0 = 91.2 kpc. In the case of M87, our analyses show that the effect of dark matter on the size of the black hole shadow is almost negligible compared to the shadow size of the Kerr vacuum solution hence the angular diameter 42 µas remains almost unaltered when the dark matter is considered. For a small totally dark matter dominated spiral such as UGC 7232, we find similar effect of dark matter on the shadow images compared to the M87. However, in specific conditions having a core radius comparable to the black hole mass and dark matter with very high density, we show that the shadow images decreases compared to the Kerr vacuum black hole. The effect of dark matter on the apparent shadow shape can shed some light in future observations as an indirect way to detect dark matter using the shadow images. Contents

In this work we investigate the consequences of running gravitational coupling on the properties of rotating black holes. Apart from the changes induced in the spacetime structure of such black holes, we also study the implications to Penrose process and geodetic precession. We are motivated by the functional form of gravitational coupling previously investigated in the context of infra-red limit of asymptotic safe gravity theory. In this approach, the involvement of a new parameterξ in this solution makes it different from Schwarzschild black hole. The Killing horizon, event horizon and singularity of the computed metric is then discussed. It is noticed that the ergosphere is increased as ξ increases. Considering the black hole solution in equatorial plane, the geodesics of particles, both null and time like cases, are explored. The effective potential is computed and graphically analyzed for different values of parameterξ . The energy extraction from black hole is investigated via Penrose process. For the same values of spin parameter, the numerical results suggest that the efficiency of Penrose process is greater in quantum corrected gravity than in Kerr Black Hole. At the end, a brief discussion on Lense-Thirring frequency is also done.

We investigate the thermodynamics of Gauss-Bonnet black holes in asymptotically de Sitter spacetimes embedded in an isothermal cavity, via a Euclidean action approach. We consider both charged and uncharged black holes, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. In the uncharged case, we find both Hawking-Page and small-to-large black hole phase transitions, whose character depends on the sign of the Gauss-Bonnet coupling. In the charged case, we demonstrate the presence of a swallowtube, signaling a compact region in phase space where a small-to-large black hole transition occurs.