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

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

1999-06-16

arxiv.org/abs/gr-qc/9906068v1

Phys.Rev. D61 (2000) 084024

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, RevTex

Scientific paper

10.1103/PhysRevD.61.084024

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.

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