Euclidean black holes and spin connection

Abstract

The Euclidean method is usually discussed in the context of the metric avoiding the typical delta of the conical singularity. We introduce a new way to calculate the Hawking temperature using the vierbein and spin connection. The conical singularity is seen globally through an effect on parallel transport, the so called holonomy of the spin connection. The period of the Euclidean time is calculated requiring that the holonomy of the spin connection is trivial at the event horizon.