Thermodynamics for Kodama observer in general spherically symmetric spacetimes

TL;DR

This paper develops a generalized thermodynamic framework for Kodama observers in spherically symmetric spacetimes, introducing a new temperature related to acceleration and analyzing the first law in dynamic black hole and cosmological contexts.

Contribution

It introduces a new Tolman temperature for Kodama observers and derives a generalized integral thermodynamics relation in non-static spherically symmetric spacetimes.

Findings

New temperature related to observer acceleration

Generalized thermodynamics relation including work terms

Application to various black hole and cosmological models

Abstract

By following the spirit of arXiv:1003.5665, we define a new Tolman temperature of Kodama observer directly related to its acceleration. We give a generalized integral form of thermodynamics relation on virtual sphere of constant $r$ in non-static spherical symmetric spacetimes. This relation contains work term contributed by `redshift work density', `pressure density' and `gravitational work density'. We illustrate it in RN black hole, Dilaton-Maxwell-Einstein black hole and Vaidya black hole. We argue that the co-moving observers are not physically related to Kodama observers in FRW universe unless in the vacuum case. We also find that a generalized differential form of first law is difficult to be well defined, and it would not give more information than the integral form.