Radiating Gravitational Collapse with Shearing Motion and Bulk Viscosity Revisited

TL;DR

This paper models the gravitational collapse of a star with anisotropic fluid, bulk viscosity, and heat flow, showing that bulk viscosity delays black hole formation and affects luminosity and stability.

Contribution

It generalizes previous collapse models by incorporating bulk viscosity and compares outcomes, highlighting effects on horizon formation and star stability.

Findings

Black hole formation is prevented due to bulk viscosity.

Luminosity reaches a maximum and then abruptly turns off.

Bulk viscosity increases system instability.

Abstract

A new model is proposed to a collapsing star consisting of an anisotropic fluid with bulk viscosity, radial heat flow and outgoing radiation. In a previous paper one of us has introduced a function time dependent into the $g_{rr}$, besides the time dependent metric functions $g_{\theta\theta}$ and $g_{\phi\phi}$. The aim of this work is to generalize this previous model by introducing bulk viscosity and compare it to the non-viscous collapse. The behavior of the density, pressure, mass, luminosity and the effective adiabatic index is analyzed. Our work is also compared to the case of a collapsing fluid with bulk viscosity of another previous model, for a star with 6 $M_{\odot}$. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the bulk viscosity the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast of the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. In contrast of the former model where the luminosity also increases exponentially, reaching a maximum and after it decreases until the formation of the black hole. The effective adiabatic index diminishes due to the bulk viscosity, thus increasing the instability of the system, in both models, in the former paper and in this work.