Hawking Radiation of Schwarzschild-de Sitter Black Hole by Hamilton-Jacobi method

TL;DR

This paper studies Hawking radiation from Schwarzschild-de Sitter black holes using a Hamilton-Jacobi tunneling approach, accounting for dynamical spacetime and self-gravitation effects, leading to a corrected emission spectrum.

Contribution

It introduces a method to analyze Hawking radiation considering dynamical backgrounds and self-gravitation, providing a correction to the traditional thermal spectrum for SdS black holes.

Findings

Tunneling rate relates to change in Bekenstein-Hawking entropy.

Emission spectrum deviates from pure thermal spectrum.

Results align with Parikh and Wilczek's correction approach.

Abstract

We investigate the Hawking radiation of Schwarzschild-de Sitter (SdS) black hole by massive particles tunneling method. We consider the spacetime background to be dynamical, incorporate the self-gravitation effect of the emitted particles and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum when energy and angular momentum are conserved. Our result is also in accordance with Parikh and Wilczek\rq s opinion and gives a correction to the Hawking radiation of SdS black hole.