Heat conduction in rotating relativistic stars

Abstract

In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation nonetheless follows from a more general, causal theory of heat propagation in which the entropy plays the role of a fluid. In deriving this result, however, we see that it is necessary to make some assumptions which are not universally valid: the dynamical timescales of the process must be long compared with the explicitly causal physics of the theory, the heat flow must be sufficiently steady, and the spacetime static. Generalising the heat equation (e.g. restoring causality) would thus entail retaining some of the terms we neglected. As a first extension, we derive the heat equation for the spacetime associated with a slowly-rotating star or black hole, showing that it only differs from the static result by an additional advection term due to the rotation, and as a consequence demonstrate that a hotspot on a neutron star will be seen to be modulated at the rotation frequency by a distant observer.