Global embedding of D-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

TL;DR

This paper explores the global embedding of various D-dimensional black holes into higher-dimensional Minkowski space to compare Hawking and Unruh temperatures, simplifying black hole physics analysis through Rindler spacetime techniques.

Contribution

It introduces the GEMS procedure for embedding black holes into Minkowski space, enabling direct comparison of Hawking and Unruh temperatures across different black hole topologies and charges.

Findings

Matching Hawking and Unruh temperatures for various black holes

Global embeddings for neutral and charged Tangherlini black holes

Analysis includes different horizon topologies and cosmological constants

Abstract

We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).