On the duality of Schwarzschild-de Sitter spacetime and moving mirror

TL;DR

This paper explores the duality between Schwarzschild-de Sitter spacetime and moving mirror models, analyzing radiation and particle spectra to understand horizon thermodynamics and quantum effects in curved spacetime.

Contribution

It introduces a novel boundary correspondence approach to study Hawking radiation in SdS spacetime, revealing non-thermal global particle distributions and asymptotic thermalization.

Findings

Particle distribution is globally non-thermal

Radiation reaches equilibrium asymptotically

Boundary dynamics elucidate horizon radiation properties

Abstract

The Schwarzschild-de Sitter (SdS) metric is the simplest spacetime solution in general relativity with both a black hole event horizon and a cosmological event horizon. Since the Schwarzschild metric is the most simple solution of Einstein's equations with spherical symmetry and the de Sitter metric is the most simple solution of Einstein's equations with a positive cosmological constant, the combination in the SdS metric defines an appropriate background geometry for semi-classical investigation of Hawking radiation with respect to past and future horizons. Generally, the black hole temperature is larger than that of the cosmological horizon, so there is heat flow from the smaller black hole horizon to the larger cosmological horizon, despite questions concerning the definition of the relative temperature of the black hole without a measurement by an observer sitting in an asymptotically flat spacetime. Here we investigate the accelerating boundary correspondence (ABC) of the radiation in SdS spacetime without such a problem. We have solved for the boundary dynamics, energy flux and asymptotic particle spectrum. The distribution of particles is globally non-thermal while asymptotically the radiation reaches equilibrium.