An exact self-similar solution for an expanding ball of radiation

TL;DR

This paper presents an exact self-similar solution to 5D Einstein equations modeling a spherically symmetric, dissipative radiation-filled universe with heat flux, exhibiting scale-invariant properties in 4D.

Contribution

It provides a novel exact 5D solution with self-similarity that describes a radiative, dissipative matter distribution in 4D, expanding previous models.

Findings

The solution satisfies energy and thermodynamic conditions.

It relates energy density and temperature via Stefan-Boltzmann law.

The model exhibits self-similar symmetry in 4D.

Abstract

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.