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Local continuity of angular momentum and noether charge for matter in general relativity

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Peer-reviewed

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Article

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Abstract

jats:titleAbstract</jats:title> jats:pConservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate of change of energy-momentum within a finite spacelike volume is equivalent to the flux integrated over the surface of this volume; for general spacetimes it is necessary to include a volume integral of a source term arising from spacetime curvature. In this work a study of continuity of matter in general relativity is extended to include angular momentum of matter and Noether currents associated with gauge symmetries. Expressions for the Noether charge and flux of complex scalar fields and complex Proca fields are found using this formalism. Expressions for the angular momentum density, flux and source are also derived which are then applied to a numerical relativity collision of boson stars in 3D with non-zero impact parameter as an illustration of the methods.</jats:p>

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Funder: Cambridge Service for Data Driven Discovery


Funder: CDT


Funder: STFC

Keywords

4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

Journal Title

Classical and Quantum Gravity

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Journal ISSN

0264-9381
1361-6382

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Publisher

IOP Publishing
Sponsorship
PRACE (2020225359)