THERMODYNAMICS OF TAUB-NUT/BOLT-ADS BLACK HOLES IN EINSTEIN–GAUSS–BONNET GRAVITY IN COUNTERTERM METHOD
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.
