Equivalence of Hawking and Unruh Temperatures and Entropies Through Flat Space Embeddings

TL;DR

This paper demonstrates that the temperature and entropy associated with horizons in curved spacetimes can be derived from their flat space embeddings, establishing a unified framework for understanding horizon thermodynamics.

Contribution

It provides a unified description of horizon temperature and entropy through higher-dimensional flat space embeddings, linking curved spacetime properties to flat space geometries.

Findings

Temperature and entropy match between curved and embedded flat spaces.

Schwarzschild horizon properties derived from flat D=6 embedding.

Unified approach applicable to true and accelerated observer horizons.

Abstract

We present a unified description of temperature and entropy in spaces with either "true" or "accelerated observer" horizons: In their (higher dimensional) global embedding Minkowski geometries, the relevant detectors have constant accelerations a_{G}; associated with their Rindler horizons are temperature a_{G}/2\pi and entropy equal to 1/4 the horizon area. Both quantities agree with those calculated in the original curved spaces. As one example of this equivalence, we obtain the temperature and entropy of Schwarzschild geometry from its flat D=6 embedding.