Hawking temperature for constant curvature black bole and its analogue in de Sitter space

TL;DR

This paper calculates the Hawking temperature of constant curvature black holes and their de Sitter space analogues using a globally embedding approach, revealing consistent temperature expressions across coordinate systems and boundary spaces.

Contribution

It introduces a method to derive Hawking temperatures for CC black holes with unusual topology, connecting their thermodynamics to boundary de Sitter spaces.

Findings

Hawking temperature matches in static and global coordinates

Temperature equals the Gibbons-Hawking temperature of boundary de Sitter space

Method applies to both CC black holes and their de Sitter counterparts

Abstract

The constant curvature (CC) black holes are higher dimensional generalizations of BTZ black holes. It is known that these black holes have the unusual topology of ${\cal M}_{D-1}\times S^1$, where $D$ is the spacetime dimension and ${\cal M}_{D-1}$ stands for a conformal Minkowski spacetime in $D-1$ dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperature takes the same form when using both the static an global coordinates. Also it is identical to the Gibbons-Hawking temperature of the boundary de Sitter spaces of these CC black holes. Employing the same approach, we obtain the Hawking temperature for the counterparts of CC black holes in de Sitter spaces.