Hawking temperature for near-equilibrium black holes

TL;DR

This paper analyzes the Hawking temperature of near-equilibrium black holes using a semiclassical approach, revealing that for slowly evolving black holes, the temperature relates to the surface gravity of the past horizon, with applications to accreting black holes and AdS spacetimes.

Contribution

Introduces a new expansion method for analyzing Hawking temperature in slowly evolving black holes, connecting temperature to past horizon surface gravity and applying it to various spacetime scenarios.

Findings

Hawking temperature is determined by the surface gravity of the past horizon for slow evolutions.

Develops a saddle point approximation method for Bogoliubov coefficients in near-equilibrium spacetimes.

Applies the framework to accreting black holes and AdS-Vaidya spacetime, with implications for AdS/CFT correspondence.

Abstract

We discuss the Hawking temperature of near-equilibrium black holes using a semiclassical analysis. We introduce a useful expansion method for slowly evolving spacetime, and evaluate the Bogoliubov coefficients using the saddle point approximation. For a spacetime whose evolution is sufficiently slow, such as a black hole with slowly changing mass, we find that the temperature is determined by the surface gravity of the past horizon. As an example of applications of these results, we study the Hawking temperature of black holes with null shell accretion in asymptotically flat space and the AdS-Vaidya spacetime. We discuss implications of our results in the context of the AdS/CFT correspondence.