Kinematic Self-Similar Heat Conducting and Charge Solutions

TL;DR

This paper classifies plane symmetric kinematic self-similar solutions of Einstein's equations for heat conducting fluids and charge dust, revealing limited solutions under various self-similarity and vector orientations.

Contribution

It provides a comprehensive classification of self-similar solutions for heat conducting and charge dust fluids in plane symmetry, identifying unique solutions in specific cases.

Findings

Only one parallel heat conducting solution exists.

All other cases reduce to perfect fluid solutions.

One unique charge dust self-similar solution found.

Abstract

The objective of this paper is to study the plane symmetric kinematic self-similar heat conducting fluid and charge dust solutions of the Einstein field equations. These solutions are classified according to self-similarity of the first, second, zeroth and infinite kinds with different equations of state. We take the self-similar vector to be tilted, orthogonal and parallel to the fluid flow. For heat conducting fluid, it is found that there exist only \emph{one} solution in parallel case. In all other possibilities, these solutions reduce to the perfect fluid kinematic self-similar solutions. For charge dust case, we also obtain only \emph{one} kinematic self-similar solution.