Local temperature for dynamical black holes

TL;DR

This paper derives a local Hawking temperature for dynamical black holes using a Hamilton-Jacobi tunneling approach, linking it to geometric surface gravity and discussing observational and final evaporation implications.

Contribution

It introduces a new local temperature definition for dynamical black holes and relates it to geometric surface gravity and observable measurements.

Findings

Derived a local Hawking temperature for dynamical horizons.

Connected the temperature to geometric surface gravity.

Discussed implications for black hole evaporation.

Abstract

A local Hawking temperature was recently derived for any future outer trapping horizon in spherical symmetry, using a Hamilton-Jacobi tunneling method, and is given by a dynamical surface gravity as defined geometrically. Descriptions are given of the operational meaning of the temperature, in terms of what observers measure, and its relation to the usual Hawking temperature for static black holes. Implications for the final fate of an evaporating black hole are discussed.