Mass function and particle creation in Schwarzschild-de Sitter spacetime

TL;DR

This paper develops a local mass function for Schwarzschild-de Sitter spacetime, linking it to black hole thermodynamics and particle creation, providing new insights into energy distribution and quantum effects in such spacetimes.

Contribution

It introduces a novel local mass function for Schwarzschild-de Sitter spacetime and connects it to thermodynamics and particle creation phenomena.

Findings

Mass function is positive, continuous, and increases with radius.

Reproduces Schwarzschild-de Sitter thermodynamics including negative pressure.

Derives particle creation linked to horizons and mass function.

Abstract

We construct a mass or energy function for the non-Nariai class Schwarzschild-de Sitter black hole spacetime in the region between the black hole and the cosmological event horizons. The mass function is local, positive definite, continuous and increases monotonically with the radial distance from the black hole event horizon. We derive the Smarr formula using this mass function, and demonstrate that the mass function reproduces the two-temperature Schwarzschild-de Sitter black hole thermodynamics, along with a term corresponding to the negative pressure due to positive cosmological constant. We further give a field theoretic derivation of the particle creation by both the horizons and discuss its connection with the mass function.