The thermodynamics of a scalar field interacting with a perfect fluid is studied, and observable consequences of the covariant variable speed of light (VSL) theory proposed by J. Magueijo are obtained. The first law of thermodyamics is modified as the scalar field becomes an additional thermodynamical variable. A recipe to obtain the modified equations of state is also obtained. After discussing the Newtonian limit and the non-relativistic hydrostatic equilibrium equation for the theory, 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 are found. 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.
Non-scalar contribution of potential in crystals
