Title: Gauge invariants of linearized gravity with a general background metric

Journal Article · Wed Nov 16 00:00:00 EST 2022 · Classical and Quantum Gravity

DOI:https://doi.org/10.1088/1361-6382/aca067· OSTI ID:1914074

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Princeton Univ., NJ (United States)
Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. Further, if the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: AC02-09CH11466; PHY 1903130

OSTI ID:: 1914074

Journal Information:: Classical and Quantum Gravity, Vol. 39, Issue 24; ISSN 0264-9381

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Gauge invariants of linearized gravity with a general background metric

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