The Relation Between the Quasi-localized Energy Complexes and the Thermodynamic Potential for the Schwarzschild-de Sitter Black Hole

Abstract

The Schwarzschild-de Sitter (SdS) black hole solution, which has two event horizons, is considered to examine the relation between the quasi-localized energy complexes on ${\cal M}$ and the heat flows passing through its boundary $\partial {\cal M}$. Here ${\cal M}$ 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 quasi-localized Einstein and M{\o}ller energy complex and the heat flows passing through the boundary is obeyed, and these two quasi-localized energy complexes could be corresponding to thermodynamic potentials.