Linear response in a charged gas in curved spacetime and covariant heat equation

TL;DR

This paper develops a covariant framework for analyzing the linear response and heat conduction of a charged relativistic gas in curved spacetime, revealing gravitational effects on heat flow near black holes.

Contribution

It introduces a second-order relativistic kinetic theory in curved spacetime and derives a covariant heat equation with novel features compared to classical models.

Findings

Derived a covariant heat equation similar to Cattaneo's but with a sign difference.

Analyzed the impact of gravity on heat conduction near a Schwarzschild black hole.

Compared behaviors of the new heat equation and the classical Cattaneo equation.

Abstract

We consider the linear response of a near-equilibrium charged relativistic gas in the presence of electromagnetic and gravitational field in a generic stationary spacetime up to the second order of relaxation time and calculate the tensorial kinetic coefficients introduced by the presence of the strong electromagnetic and/or gravitational field. Using the covariant transfer equations thus developed, a covariant heat equation governing the relativistic heat conduction is derived, which, in Minkowski spacetime, reduces into a form which is remarkably similar to the well-known Cattaneo equation but with a different sign in front of the second-order time derivative term. We also perform a comparative analysis on the different behaviors of our heat equation and the Cattaneo equation in Minkowski spacetime. Furthermore, the effect of gravity on the heat conduction predicted by our heat equation is illustrated around Schwarzschild black hole, which makes a sharp contrast to the Minkowski case.