Mixed potentials in radiative stellar collapse

TL;DR

This paper derives new exact solutions for radiating, shearing, geodesic stars during gravitational collapse, allowing mixed spatial-temporal metric functions without prior assumptions, expanding the understanding of stellar evolution models.

Contribution

It introduces a systematic method to generate new classes of solutions with mixed dependencies, extending previous models without assuming separability or fixed temporal evolution.

Findings

New exact solutions with mixed spatial and temporal dependence.

Recovery of previously known models as special cases.

Demonstration of a Riccati equation approach to junction conditions.

Abstract

We study the behaviour of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational potentials or initially fixing the temporal evolution of the model unlike earlier treatments. A systematic approach enables us to write the junction condition as a Riccati equation which under particular conditions may be transformed into a separable equation. New classes of solutions are generated which allow for mixed spatial and temporal dependence in the metric functions. We regain particular models found previously from our general classes of solutions.