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 none the less 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. Generalizing 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 slowlyrotating 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.
Original language  English 

Pages (fromto)  42074215 
Number of pages  9 
Journal  Monthly Notices of the Royal Astronomical Society 
Volume  479 
Issue number  3 
Early online date  29 Jun 2018 
DOIs  
Publication status  Published  21 Sep 2018 
Externally published  Yes 
Keywords
 Accretion, accretion discs
 Conduction
 Gravitation
 Stars: rotation
 Stars: neutron
Profiles

Samuel Lander
 School of Engineering, Mathematics and Physics  Lecturer in Physics
Person: Academic, Teaching & Research