We consider scalar and axial gravitational perturbations of black hole solutions in brane world scenarios. We show that perturbation dynamics is surprisingly similar to the Schwarzschild case with strong indications that the models are stable. Quasinormal modes and late-time tails are discussed. We also study the thermodynamics of these scenarios verifying the universality of Bekensteins entropy bound as well as the applicability of t Hoofts brickwall method.
Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an extern
al electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.
We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and fo
r thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $ell$ is defined by the formula $ell=Lexp(gamma_0)$, where $L$ is the coordinate length of the strut, and $gamma_0$ is the value of the metric function $gamma$ on the strut.
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.
Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordstro
m black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $ell$ turns out to be defined by the same simple formula $ell=Lexp(gamma_0)$, $L$ being the coordinate length of the strut and $gamma_0$ the value of the metric function $gamma$ on the strut, which permits the elaboration of $ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.