Radiating Spherical Collapse for an Inhomogeneous Interior Solution

TL;DR

This paper investigates gravitational collapse of inhomogeneous, viscous fluid spheres matched to an exterior Vaidya spacetime, exploring conditions for non-singular outcomes and effects of electromagnetic Lagrangians on collapse behavior.

Contribution

It introduces a detailed matching framework for inhomogeneous interior solutions with viscous fluids and analyzes how electromagnetic Lagrangians influence singular or non-singular collapse outcomes.

Findings

Non-singular objects possible under specific initial conditions.

Electromagnetic Lagrangians affect the collapse's final stage.

Energy conditions influence the collapse process.

Abstract

We analyze the problem of gravitational collapse considering the matching of an exterior region described by the Vaidya's metric and an interior region described by a spherically symmetric shear-free inhomogeneous geometry sourced by a viscous fluid. We establish initial and final conditions for the process in order that the outcome be a non-singular object, when this is possible, and check how it depends on the fulfillment of the energy conditions. We then apply explicitly the matching procedure to the cases of linear and nonlinear Lagrangians describing electromagnetic fields inside the star, and analyze how the different behaviors for the scale factor of the interior geometry produce singular or nonsingular final stages of the collapse depending on the range where the initial conditions lie.