Black hole evaporation in de Sitter space

TL;DR

This paper studies the evaporation of Kerr-de Sitter black holes, analyzing greybody factors, superradiance, and entropy evolution, revealing that black holes spin down rapidly and entropy increases, consistent with thermodynamics.

Contribution

It provides new analytic calculations of greybody factors and superradiance effects in Kerr-de Sitter space, and examines the entropy evolution during black hole evaporation.

Findings

Cosmological constant reduces superradiance amplification.

Black holes spin down rapidly before complete evaporation.

Total entropy increases, confirming the generalized second law.

Abstract

We investigate the evaporation process of a Kerr-de Sitter black hole with the Unruh-Hawking-like vacuum state, which is a realistic vacuum state modelling the evaporation process of a black hole originating from gravitational collapse. We also compute the greybody factors for gravitons, photons, and conformal-coupling massless scalar particles by using the analytic solutions of the Teukolsky equation in the Kerr-de Sitter background. It turns out that the cosmological constant quenches the amplification factor and it approaches to zero towards the critical point where the Nariai and extremal limits merge together. We confirm that even near the critical point, the superradiance of gravitons is more significant than that of photons and scalar particles. Angular momentum is carried out by particles several times faster than the mass energy decreases. This means that a Kerr-de Sitter black hole rapidly spins down to a nearly Schwarzschild-de Sitter black hole before it completely evaporates. We also compute the time evolution of the Bekenstein-Hawking entropy. The total entropy of the Kerr-de Sitter black hole and cosmological horizon increases with time, which is consistent with the generalized second law of thermodynamics.