Thermodynamics in variable speed of light theories

TL;DR

This paper explores the thermodynamics of a covariant variable speed of light theory, deriving modified laws, equations of state, and limits on the variation of the speed of light from astrophysical observations.

Contribution

It provides a comprehensive thermodynamic framework for variable speed of light theories and derives astrophysical bounds on the variation of $c$ using observational data.

Findings

Derived modified first law of thermodynamics for the theory

Obtained bounds on the variation of the speed of light from Mercury's radius and white dwarf luminosity

Established limits on $c$ variation consistent with observational constraints

Abstract

The perfect fluid in the context of a covariant variable speed of light theory proposed by J. Magueijo is studied. On the one hand the modified first law of thermodynamics together with a recipe to obtain equations of state are obtained. On the other hand the Newtonian limit is performed to obtain the nonrelativistic hydrostatic equilibrium equation for the theory. The results obtained are used to determine the time variation of the radius of Mercury induced by the variability of the speed of light ($c$), and the scalar contribution to the luminosity of white dwarfs. Using a bound for the change of that radius and combining it with an upper limit for the variation of the fine structure constant, a bound on the time variation of $c$ is set. An independent bound is obtained from luminosity estimates for Stein 2015B.