Topological nature of the Hawking temperature of black holes

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 twodimensional 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.

Hawking radiation via Gauss–Bonnet theorem

“…As mentioned before, the method of RVB [1] computes the black hole temperature in a simple way via the 2dimensional Euler characteristic and the Gauss-Bonnet theorem [1,2]. To understand the formalism of the RVB, let us first consider the following 4-dimensional spherically symmetric and static black hole metric…”

“…The topological formula for the Hawking temperature of the above two-dimensional black holes has been recently invented by the RVB [1,2] and it s given by…”

“…Recently, Robson, Villari, and Biancalana (RVB) have shown that Hawking temperature of a black hole can also be topologically derived [1,2] such as obtaining the entropy of the black hole from topology [35,36]. The method of RVB is based on the Gauss-Bonnet theorem and the Euler characteristic, which are invariants of the topology.…”

“…In this work, we shall apply the RVB method [1] to various spacetimes of black holes such as dyonic Reissner-Nordström black hole, Schwarzschild-electromagnetic black hole, quantum corrected black hole, Schwarzschildlike black hole in a bumblebee gravity model and linear dilaton black hole. For this purpose, first we briefly review the RVB method in the following section.…”

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In this paper, we apply the recently found breakthrough topological method of Robson, Villari and Biancalana (RVB) [1,2] to the various black holes to derive their Hawking temperature. We show that the RVB method can easily be employed to compute the Hawking temperature of black holes having spherically symmetric topology.

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