General relativistic heat flow from first order hydrodynamics

TL;DR

This paper derives the heat flow equation in a relativistic setting with gravity, analyzing temperature and chemical potential profiles around various black hole spacetimes using a new stable first-order hydrodynamics framework.

Contribution

It introduces the heat flow equation in a relativistic, gravitational context based on a recently developed stable first-order hydrodynamics theory.

Findings

Heat flux times redshift factor is conserved in static and stationary backgrounds.

Temperature profiles are obtained for different black hole spacetimes.

Chemical potential profiles are also discussed.

Abstract

Following the recently proposed stable and causal first-order relativistic hydrodynamics by Bemfica, Disconzi, and Noronha, we find the heat flow equation in the presence of gravity for a non-viscous fluid, which suffers heat dissipation. The derivation is confined to static and stationary backgrounds. We find that in the presence of gravity, the heat flux times a redshift factor is conserved. Then for radial heat flow, the temperature profiles are obtained from the heat equation when the gravity is sourced by Schwarzschild, Schwarzschild-dS, Kerr and Kerr-dS black holes, respectively. Consequently, the chemical potential profile is also discussed.