Scattering amplitudes and thermal temperatures of the Schwarzschild-de Sitter black holes

TL;DR

This paper investigates the thermodynamic properties and scattering amplitudes of Schwarzschild-de Sitter black holes, deriving relations between horizon temperatures using low energy perturbation theory.

Contribution

It introduces a method to compute scattering amplitudes and horizon temperatures for small black holes in de Sitter space using low energy perturbation analysis.

Findings

Derived scattering amplitudes for scalar fields near horizons

Calculated thermal temperatures from scattering data

Established a relation between black hole and cosmological horizon temperatures

Abstract

We study thermodynamic evaporation of Schwarzschild-de Sitter black holes in terms of a low energy perturbation theory. A small black hole which is far from the cosmological horizon and observers at the spacelike hypersurface where black hole attraction and expansion of cosmological horizon balance exactly are considered. In the low energy perturbation, scalar field equations are solved in both regions of the hypersurface and scattering amplitudes are derived. And then the desired thermal temperatures from the two horizons are obtained as a ``minimal'' value of the statistical thermal temperature, and the fine-tuning between amplitudes gives a relation of the two temperatures.