A stellar model with diffusion in general relativity

TL;DR

This paper develops a spherically symmetric stellar model in general relativity with a diffusing pressureless fluid, showing that diffusion enforces homogeneity and prevents naked singularities, and explores matching to an exterior metric and the causal structure of a self-similar solution.

Contribution

It introduces a novel stellar model with diffusion in general relativity, demonstrating effects on homogeneity, singularity formation, and exterior matching.

Findings

Diffusion enforces spatial homogeneity in the stellar interior.

No naked singularities form in the diffusion-influenced collapse.

The exterior can be matched to a modified Vaidya metric with variable cosmological constant.

Abstract

We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution.