Heat conduction in general relativity

TL;DR

This paper develops a new relativistic heat conduction model using Carter's variational approach, introducing binormal contributions, resulting in novel heat-flow equations and insights into system stability.

Contribution

It presents a new heat conduction equation in general relativity that incorporates binormal degrees of freedom and proposes a physical ansatz for system evolution.

Findings

Discovered new heat-flow equations with binormal contributions.

Identified additional 'Klein' modes affecting stability.

Found stability conditions are less restrictive than previous models.

Abstract

We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential. We pay attention to the fact that there are two additional degrees of freedom in choosing the relativistic analog of Cattaneo equation for the parts binormal to the caloric and the number flows. Including the contributions from the binormal parts, we find a $\textit{new}$ heat-flow equations and discover their dynamical role in thermodynamic systems. The benefit of introducing the binormal parts is that it allows room for a physical ansatz for describing the whole evolution of the thermodynamic system. Taking advantage of this platform, we propose a proper ansatz that deals with the binormal contributions starting from the physical properties of thermal equilibrium systems. We also consider the stability of a thermodynamic system in a flat background. We find that $\textit{new}$ "Klein" modes exist in addition to the known ones. We also find that the stability requirement is less stringent than those in the literature.