  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.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology