Multi-dimensional simple waves in fully relativistic fluids

Multi-dimensional simple waves built on the basis of the Boillat condition are employed for fully relativistic fluid and plasma flows. Three essential modes, namely the vortex, the entropy and sound modes, are derived where each of them is different from its non-relativistic analogue. The vortex and entropy modes are formally solved in both the laboratory and wave frame (co-moving with the wavefront) to yield a few classical solutions. It is shown that by making a suitable transformation to the wave frame, it will be possible to exactly solve the sound mode at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solutions is introduced and determined. Finally, a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. The derived symmetry properties and their corresponding fundamental invariants are shown to create a wide variety of classical solutions; some of them may have physical interest.