Embedding into flat spacetime and black hole thermodynamics

TL;DR

This paper demonstrates that black hole thermodynamics, including temperature and entropy, can be derived from their embedding into higher-dimensional flat spacetime, providing a new perspective using flat spacetime field theory.

Contribution

It shows how black hole temperature and entropy can be obtained from embedding into flat spacetime, offering a novel thermodynamic interpretation.

Findings

Black hole temperature can be derived from embedding into flat spacetime.

Black hole entropy's area law can be obtained via flat spacetime field theory.

Embedding provides a new framework for black hole thermodynamics.

Abstract

It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes \'{a} la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacetime it is indeed possible to arrive at the area scaling law for black hole entropy. Thus using flat spacetime field theory, one can indeed provide a thermodynamic description of black holes. Implications are also discussed.