Multidimensional simple waves in fully relativistic fluids

TL;DR

This paper extends the theory of multidimensional simple waves to fully relativistic fluids, deriving new modes and solutions, and analyzing symmetries and invariants in relativistic plasma flows.

Contribution

It introduces a relativistic extension of simple wave solutions, deriving vortex, entropy, and sound modes, and performs symmetry analysis for these relativistic wave equations.

Findings

Derived vortex, entropy, and sound modes in relativistic fluids.

Solved vortex and entropy modes in laboratory and wave frames.

Analyzed symmetries and invariants of the vortex mode equation.

Abstract

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.