Thermal dynamics in general relativity

Source abstract

We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focusing on the pure heat conduction problem, we compare the variational results with the second-order model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first-order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime.