The Relation between the Quasi-Localized Energy-Momentum Complexes and the Thermodynamic Potential for the Schwarzschild-de Sitter Black Hole

I-Ching Yang

doi:10.1155/2017/2482940

Abstract

The Schwarzschild-de Sitter black hole solution, which has two event horizons, is considered to examine the relation between the energy component of quasi-localized energy-momentum complexes on M and the heat flows passing through its boundary ∂M. Here M is the patch between cosmological event horizon and black hole event horizon of the SdS black hole solution. Conclusively, the relation, like the Legendre transformation, between the energy component of quasi-localized Einstein and Møller energy-momentum complex and the heat flows passing through the boundary is obeyed, and these two energy components of quasi-localized energy-momentum complexes could be corresponding to thermodynamic potentials.

Highlights

Yang et al [1,2,3] have inferred that the formula about the quasi-localized Einstein and Møller energy-momentum complexes on M∗ and the heat flows passing through the boundary of M∗ are related as
M∗ is the patch between event horizon H+ located at r = r+ and inner Cauchy horizon H− located at r = r− for the spherically symmetric black hole with two separate horizons
I consider the Schwarzschild-de Sitter (SdS) black hole solution, which has two separate event horizons, and a review of relation between the energy component of quasi-localized energy-momentum complexes on a patch between two event horizons and the heat flows passing through its boundary

Summary

Introduction

Yang et al [1,2,3] have inferred that the formula about the quasi-localized Einstein and Møller energy-momentum complexes on M∗ and the heat flows passing through the boundary of M∗ are related as. M∗ is the patch between event horizon H+ located at r = r+ and inner Cauchy horizon H− located at r = r− for the spherically symmetric black hole with two separate horizons. There was a controversy that an acceptable definition exists for the temperature and entropy of black hole at Cauchy horizon. I consider the Schwarzschild-de Sitter (SdS) black hole solution, which has two separate event horizons, and a review of relation between the energy component of quasi-localized energy-momentum complexes on a patch between two event horizons and the heat flows passing through its boundary

The Schwarzschild-de Sitter Black Hole Metric

The Quasi-Localized Energy-Momentum Complexes

Conclusion