Taking the Temperature of a Black Hole

TL;DR

This paper introduces a method to define a local temperature for free-falling observers near black holes using higher-dimensional embeddings, revealing that such observers do not detect high-temperature radiation even around high-temperature black holes.

Contribution

It presents a novel approach to measure local temperature in black hole spacetimes using global embeddings, providing insights into observer-dependent thermal perceptions.

Findings

Free-fall temperature remains finite at the event horizon.

Observers outside an AdS black hole do not perceive high-temperature radiation.

The local temperature approaches Hawking temperature at infinity.

Abstract

We use the global embedding of a black hole spacetime into a higher dimensional flat spacetime to define a local temperature for observers in free fall outside a static black hole. The local free-fall temperature remains finite at the event horizon and in asymptotically flat spacetime it approaches the Hawking temperature at spatial infinity. Freely falling observers outside an AdS black hole do not see any high-temperature thermal radiation even if the Hawking temperature of such black holes can be arbitrarily high.