Thermal dynamics in general relativity

Abstract

We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focusing on the pure heat conduction problem, we compare the variational results with the secondorder model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first-order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime.

Quantised vortices and mutual friction in relativistic superfluids

“…In a multi-component system the choice of frame is less obvious. This is clearly illustrated by the classic problem of relativistic heat-flow [27,28].…”

“…Hence, we base our discussion on Carter's convective variational principle [26], which allows for an arbitrary number of interpenetrating fluid components. In the last few years, this strategy has led to progress on problems involving relativistic superfluids [29][30][31], the vexing issue of causality in heat flow [27,28], elastic systems [32,33], non-ideal magnetohydrodynamics [34] as well providing new insights into dissipative fluid systems [35].…”

“…Assuming that the two fluids are coupled by friction [27,28], we have two coupled equations of motion [35] …”

A variational approach to resistive relativistic plasmas

“…issues arising when components become superfluid, when heat flows and when the electromagnetic charge current is treated as a dynamical variable [1, [9][10][11]. These advances allow us to consider a wide range of relevant phenomena, but the general theory is incomplete in two important respects.…”

Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

“…The special relativistic generalization of Newtonian hydrodynamics has attracted much attention in both statistical physics and high energy physics since its early days [1][2][3][4][5][6][7] and has found applications in a wide range of physical processes from astrophysical phenomena [8][9][10], to the hydrodynamic description of the high temperature quark-gluon (QG) plasma in the heavy-ion collision experiments at CERN and BNL [11,12], to the recent studies on graphene [13][14][15][16]. Indeed, the growing interest in relativistic hydrodynamic (RH) is not restricted to the hydrodynamics of perfect fluids [7,17] but also extends to dissipative description of relativistic systems [8,[18][19][20][21][22][23] Despite its long history and wide usage, there are still disagreements on the fundamental postulates and definitions of the theory, specifically in the presence of dissipative effects.…”