Thermodynamics for Kodama observer in general spherically symmetric spacetimes

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.

18 pages, typos corrected, references added

References in corpus (1)

• On the Origin of Gravity and the Laws of Newton

Cited by in corpus (4)

• Unruh--DeWitt detectors in spherically symmetric dynamical space-times
• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• On the Unruh effect in de Sitter space
• Unruh-DeWitt detector and the interpretation of the horizon temperature in spherically symmetric dynamical space-times