Gauge invariants of linearized gravity with a general background metric
arXiv:2105.04680 · doi:10.1088/1361-6382/aca067
Abstract
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 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 \textit{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 gravitational waves in~vacuum. For a general background, this operator is expressed in terms of the Green's operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.
References in corpus (43)
- Cosmological perturbations
- The basics of gravitational wave theory
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests
- Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
- On the Gauge Invariance of Cosmological Gravitational Waves
- Gravitational spin Hall effect of light
- Gravitational Waves in Cold Dark Matter
- Damping of gravitational waves by matter
- Quantization of linearized gravity in cosmological vacuum spacetimes
- Quasioptical modeling of wave beams with and without mode conversion: I. Basic theory
- Gauge invariant formulation of gravitational waves in metric gravity
- Gauge-invariant quantum gravitational corrections to correlation functions
- Non-linear gravitational wave interactions with plasmas
- Gravitational and magnetosonic waves in gamma-ray bursts
- Photon frequency conversion induced by gravitational radiation
- Gauge Invariant Perturbations of the Schwarzschild Spacetime
- Parametric Excitation of Alfven Waves by Gravitational Radiation
- On the propagation of gravitational waves in strong magnetic fields
- Cyclotron damping and Faraday rotation of gravitational waves
- Propagators for gauge-invariant observables in cosmology
- Gravitational Landau Damping for massive scalar modes
- Quasilinear theory for inhomogeneous plasma
- Testing the warmness of dark matter
- Riemann Normal Coordinates, Smooth Lattices and Numerical Relativity
- Ponderomotive dynamics of waves in quasiperiodically modulated media
- Cosmological Perturbations and Invariant Observables in Geodesic Lightcone Coordinates
- The interaction of gravitational waves with strongly magnetized plasmas
- Wave-kinetic approach to zonal-flow dynamics: recent advances
- Compactly supported linearised observables in single-field inflation
- The Cosmological Perturbation Theory on the Geodesic Light-Cone background
- Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime
- Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
- Compatibility complex for black hole spacetimes
- Interaction between gravitational waves and plasma waves in the Vlasov description
- Generation of Gravitational Radiation in Dusty Plasmas and Supernovae
- Approaches to linear local gauge-invariant observables in inflationary cosmologies
- Gravitational wave modes in matter
- Dispersion of gravitational waves in cold spherical interstellar medium
- Comments on gauge-invariance in cosmology
- Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
- Equivalence between the Weyl-tensor and gauge-invariant graviton two-point functions in Minkowski and de Sitter spaces
- Average nonlinear dynamics of particles in gravitational pulses: effective Hamiltonian, secular acceleration, and gravitational susceptibility