Analytical models for gravitating radiating systems

TL;DR

This paper develops new analytical models for spherically symmetric, heat-conducting relativistic fluids under gravity, deriving solutions that are physically consistent and expressed with elementary functions.

Contribution

It introduces novel classes of solutions for gravitating radiating systems by solving a nonlinear differential equation with real metric functions.

Findings

Solutions are well-behaved with realistic pressure and density profiles.

A complex transformation yields an exact real-valued metric solution.

Models are compatible with a core-envelope structure.

Abstract

We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework.