Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior

TL;DR

This paper develops a gauge-invariant, coordinate-independent framework for analyzing small non-spherical perturbations in collapsing stars, enabling better modeling of gravitational wave production during supernovae.

Contribution

It introduces a covariant, scalarized perturbation formalism for spherically symmetric, time-dependent spacetimes with perfect fluid matter, extending previous methods to include a complete set of gauge-invariant degrees of freedom.

Findings

Derived covariant, gauge-invariant perturbation equations for stellar collapse.

Identified true degrees of freedom with free initial data for axial and polar perturbations.

Established evolution equations for these degrees of freedom, facilitating gravitational wave analysis.

Abstract

Small non-spherical perturbations of a spherically symmetric but time-dependent background spacetime can be used to model situations of astrophysical interest, for example the production of gravitational waves in a supernova explosion. We allow for perfect fluid matter with an arbitrary equation of state p=p(rho,s), coupled to general relativity. Applying a general framework proposed by Gerlach and Sengupta, we obtain covariant field equations, in a 2+2 reduction of the spacetime, for the background and a complete set of gauge-invariant perturbations, and then scalarize them using the natural frame provided by the fluid. Building on previous work by Seidel, we identify a set of true perturbation degrees of freedom admitting free initial data for the axial and for the l>1 polar perturbations. The true degrees of freedom are evolved among themselves by a set of coupled wave and transport equations, while the remaining degrees of freedom can be obtained by quadratures. The polar l=0,1 perturbations are discussed in the same framework. They require gauge fixing and do not admit an unconstrained evolution scheme.