Gravitational waves in Friedman-Lemaitre-Robertson-Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle

Abstract

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman-Lemaitre-Robertson-Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single "master equation" that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.

misprints corrected, matches version published in Classical and Quantum Gravity

References in corpus (5)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Relativistic cosmology and large-scale structure
• Stochastic gravitational waves associated with the formation of primordial black holes
• Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform
• Evolution of linear perturbations in Lemaître-Tolman-Bondi void models

Cited by in corpus (10)

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• Axial gravitational waves in FLRW cosmology and memory effects
• Cosmological perturbations in the Regge-Wheeler formalism
• Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe
• Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes
• Huygens' principle for the generalized Dirac operator in curved spacetime
• Axial Gravitational Waves in Bianchi I Universe
• On the propagation of gravitational waves in matter-filled Bianchi I universe
• A possible new cosmological redshift effect due to $\Lambda$ on traveling gravitational waves in Friedmann universes