Hawking radiation in multi-horizon spacetimes using Hamilton Jacobi method

TL;DR

This paper applies the Hamilton-Jacobi method to compute Hawking temperatures in multi-horizon spacetimes, emphasizing the role of horizon contributions and effective surface gravity in radiation processes.

Contribution

It demonstrates the use of Hamilton-Jacobi method for calculating Hawking temperature in various multi-horizon spacetimes, confirming the importance of horizon contributions.

Findings

Hawking temperature depends on contributions from multiple horizons

Effective surface gravity determines radiation temperature

Method applies to Schwarzschild-de Sitter, RNdS, and rotating BTZ black holes

Abstract

It has been recently shown that the contribution between the horizons determines the Hawking temperature for a multi-horizon spacetime. In this article, we apply the Hamiltonian Jacobi method to compute the Hawking temperature for some multi-horizon spacetimes like Schwarzschild-de Sitter spacetime (SdS), Reissner-Nordstrom-de Sitter spacetime (RNdS), and rotating BTZ black hole spacetime (RBTZ) and also arrive at the same conclusion. There are two contributions to the tunneling process of radiation. The combination of these two contributions gives the radiation with the Hawking temperature with an effective surface gravity.