Symmetry group analysis of relativistic heat conducting fluids

TL;DR

This paper analyzes the symmetry groups of relativistic heat-conducting fluids using Lie group methods, comparing Eckart and Israel-Stewart theories, and finds physically acceptable solutions with exponential velocity decay.

Contribution

It provides the first symmetry group analysis for 1+1D relativistic heat-conducting fluids in both Eckart and Israel-Stewart frameworks, highlighting their solution structures.

Findings

Both models admit physically acceptable solutions with exponential decay in velocity.

The symmetry analysis reveals differences in solution structures between the two theories.

Group-invariant solutions demonstrate the models' viability under specific initial conditions.

Abstract

The Lie symmetry group for 1+1 dimensional relativistic heat-conducting fluid is calculated for two different theories, Eckart and Israel-Stewart and a comparison between the group-invariant solutions has been made. Both fluids were founded to be physical acceptable in the sense that during the evolution of the fluid there are three velocity solutions that are decreasing exponentially for particular choices of the initial conditions.