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

Gauge-invariant and coordinate-independent perturbations of stellar collapse: the interior
Gauge-invariant and coordinate-independent perturbations of stellar collapse: the interior
Small nonspherical 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(?,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>~2 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.
1550-7998
084024-[17pp]
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martin-Garcia, José M.
98ce3629-0c09-4223-8098-40e64b22b837
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martin-Garcia, José M.
98ce3629-0c09-4223-8098-40e64b22b837

Gundlach, Carsten and Martin-Garcia, José M. (2000) Gauge-invariant and coordinate-independent perturbations of stellar collapse: the interior. Physical Review D, 61 (8), 084024-[17pp]. (doi:10.1103/PhysRevD.61.084024).

Record type: Article

Abstract

Small nonspherical 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(?,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>~2 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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Published date: 2000

Identifiers

Local EPrints ID: 29184
URI: https://eprints.soton.ac.uk/id/eprint/29184
ISSN: 1550-7998
PURE UUID: ec63a3ca-bd53-486d-8f88-55050bffef22
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 18 Jul 2006
Last modified: 20 Jul 2018 00:34

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