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.Comment: Updated version with more relevant reference
