On the Topological Nature of the Hawking Temperature of Black Holes

TL;DR

This paper reveals that the Hawking temperature of black holes has a topological origin, expressible through the Euler characteristic, enabling a simple covariant computation applicable to various black hole metrics.

Contribution

It introduces a topological formula based on the Euler characteristic to compute Hawking temperature for two-dimensional black holes and related metrics, simplifying previous methods.

Findings

The Hawking temperature can be derived from topological invariants.

The formula applies to any 2D black hole and dimensionally reduced metrics.

Validated on multiple black hole systems and soliton emissions.

Abstract

In this work we determine that the Hawking temperature of black holes possesses a purely topological nature. We find a very simple but powerful formula, based on a topological invariant known as the Euler characteristic, which is able to provide the exact Hawking temperature of any two-dimensional black hole -- and in fact of any metric that can be dimensionally reduced to two dimensions -- in any given coordinate system, introducing a covariant way to determine the temperature only using virtually trivial computations. We apply the topological temperature formula to several known black hole systems as well as to the Hawking emission of solitons of integrable equations.