Entropy and temperatures of Nariai black hole

TL;DR

This paper calculates the statistical entropy of the Nariai black hole using the brick-wall method, showing it adheres to the area law and discussing implications for black hole thermodynamics.

Contribution

It demonstrates that the entropy of the Nariai black hole follows the area law despite temperature dependence on Killing vector choice, aligning with Wald entropy.

Findings

Entropy follows the area law regardless of temperature dependence.

Temperature varies with the choice of Killing vector but does not affect entropy.

Results have implications for understanding black hole thermodynamics.

Abstract

The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the time-like Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.