Radiating relativistic matter in geodesic motion

TL;DR

This paper analyzes the gravitational behavior of a radiating star with particles in geodesic motion, providing new exact solutions and exploring their physical and thermal properties.

Contribution

It introduces a simplified analytic approach transforming the governing equations into solvable forms, yielding a broad family of solutions including known models.

Findings

Solutions include Minkowski and Friedmann dust spacetimes as special cases.

Derived temperature profiles for specific models.

Presented exact solutions using elementary and special functions.

Abstract

We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find that Bernoulli, Riccati and confluent hypergeometric equations are possible. These admit solutions in terms of elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Our infinite family of solutions contains specific models found previously. For a particular metric we briefly investigate the physical features, derive the temperature profiles and plot the behaviour of the casual and acasual temperatures.