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

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}/2πand 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.