Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior

TL;DR

This paper develops boundary conditions for gauge-invariant perturbations of collapsing stars, enabling matching of interior fluid perturbations to exterior Schwarzschild spacetime, advancing the understanding of stellar collapse dynamics.

Contribution

It introduces boundary conditions for gauge-invariant perturbations at the star's surface, linking interior collapse models to exterior vacuum solutions.

Findings

Derived boundary conditions for interior-exterior perturbation matching.

Established a formalism for gauge-invariant perturbations in stellar collapse.

Enhanced modeling of gravitational perturbations during star collapse.

Abstract

In Paper I in this series we constructed evolution equations for the complete gauge-invariant linear perturbations of a time-dependent spherically symmetric perfect fluid spacetime. A key application of this formalism is the interior of a collapsing star. Here we derive boundary conditions at the surface of the star, matching the interior perturbations to the well-known perturbations of the vacuum Schwarzschild spacetime outside the star.