Black hole in de Sitter space

TL;DR

This paper investigates the topology and thermal properties of black holes in de Sitter space, revealing complexities in their Euclidean structure and limitations of traditional methods for multi-horizon spacetimes.

Contribution

It introduces a global topological approach to analyze Schwarzschild-de Sitter black holes and highlights the failure of local conical singularity methods in multi-horizon scenarios.

Findings

Topological method relates Euler number to Gibbons-Hawking temperature.

Euclidean topology of de Sitter black holes is more complex than previously thought.

Local conical singularity approach fails for multi-horizon black hole spacetimes.

Abstract

If cosmological constant is positive, a black hole is naturally described by the Schwarzschild-de Sitter solution with two horizons. We use the global method to extract the topological information and the selection rule for the Gibbons-Hawking temperature for the thermal vacua. These are related to the Euler number of the Euclidean section whose topology is more complicated than expected. We also point out the failure of the usual local method of conical singularity approach in dealing with multi-horizon scenarios.