Towards a causal (effective) thermodynamics of scalar-tensor gravity

Abstract

The thermal analogy between the effective fluid of scalar-tensor gravity and Eckart's irreversible thermodynamics is extended to the causal Israel-Stewart model, adopting the minimal ansatz of promoting the heat flux density to a timelike vector. This choice yields analytically manageable constitutive equations, allowing for the first consistent decoupling of the effective temperature ${\calT}$ and the effective thermal conductivity ${\cal K}$ of scalar-tensor gravity. Crucially, this new framework preserves the interpretation of general relativity as the equilibrium state approached via a dynamical relaxation process in the vanishing-${\cal K T}$ limit. This new causal formalism is finally applied to exact solutions in cosmology.