Affiliation:
1. School of Liberal Arts and Sciences, Korea National University of Transportation , Daehakro 50, Chungju, 27469 , Republic of Korea
Abstract
Abstract
We investigate the steady state of heat conduction in general relativity using a variational approach for two-fluid dynamics. We adopt coordinates based on the Landau–Lifschitz observer because it allows us to describe thermodynamics with heat, formulated in the Eckart decomposition, on a static geometry. Through our analysis, we demonstrate that the stability condition of a thermal equilibrium state arises from the fundamental principle that heat cannot propagate faster than the speed of light. We then formulate the equations governing steady-state heat conduction and introduce a binormal equilibrium condition that the Tolman temperature gradient holds for the directions orthogonal to the heat flow. As an example, we consider radial heat conductions in a spherically symmetric spacetime. We find that the total diffusion over a spherical surface satisfies a red-shifted form, $J(r) \sqrt{-g_{tt}} =$ constant. We also discuss the behavior of local temperature around an event horizon and specify the condition that the local temperature is finite there.
Funder
National Research Foundation
Publisher
Oxford University Press (OUP)
Subject
General Physics and Astronomy