Narrow Results

We prove that the thermodynamic properties of a Schwarzschild black hole are unaffected by an external magnetic field passing through it. Apart from the background subtraction prescription, this result is also obtained by using a counterterm method.

The dilatonic Ernst solution describing a Schwarzschild black hole immersed in a background magnetic field is generalized by including a Liouville-type potential in the action principle. We prove that the thermodynamic properties of this new black hole dilaton solution are unaffected by an external magnetic field passing through it.

We give a review of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity in six dimensions. Although the spacetime with base space S² × S² has a curvature singularity at r = N, which does not admit NUT solutions, we may proceed with the same computations as in the ℂℙ² case. The investigation of thermodynamics of NUT/bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole in counterterm method. Then the validity of the first law of thermodynamics is demonstrated. Stability analysis is done by investigating the heat capacity and entropy in the allowed range. For NUT solution, there exists a stable phase at a narrow range and in bolt solutions, the metric is completely stable for S² × S² and is completely unstable for the ℂℙ² case.