Boosting gravitational waves: a review of kinematic effects on amplitude, polarization, frequency and energy density
Abstract: We review the kinematic effects on a gravitational wave due to either a peculiar motion of the astrophysical source emitting it or a local motion of the observer. Working in the context of general relativity, we show at fully non-linear order in velocity, that the amplitude of the wave is amplified by the Doppler factor in the case in which the source moves with respect to a reference frame, while it is invariant if the observer moves (with respect to a reference observer). However, the observed specific intensity transforms in the same way under a boost of the source or of the observer. We also show at fully non-linear order that under a boost (of either source or observer), the polarization tensor is rotated in the same way the wave direction is rotated by aberration, such that the only net effect of a boost on polarization is to change the phase of the helicity components. We apply these results to a wave emitted by a binary system of compact objects in the cosmological context.
- L. Sberna et al., Observing GW190521-like binary black holes and their environment with LISA, Phys. Rev. D 106, 064056 (2022), arXiv:2205.08550 [gr-qc] .
- G. Cusin and G. Tasinato, Doppler boosting the stochastic gravitational wave background, JCAP 08 (08), 036, arXiv:2201.10464 [astro-ph.CO] .
- G. Tasinato, Kinematic anisotropies and pulsar timing arrays, Phys. Rev. D 108, 103521 (2023), arXiv:2309.00403 [gr-qc] .
- R. Stiskalek, J. Veitch, and C. Messenger, Are stellar–mass binary black hole mergers isotropically distributed?, Mon. Not. Roy. Astron. Soc. 501, 970 (2021), arXiv:2003.02919 [astro-ph.HE] .
- N. Sugiura, N. Sugiyama, and M. Sasaki, Anisotropies in Luminosity Distance, Progress of Theoretical Physics 101, 903 (1999).
- L. Hui and P. B. Greene, Correlated Fluctuations in Luminosity Distance and the (Surprising) Importance of Peculiar Motion in Supernova Surveys, Phys. Rev. D 73, 123526 (2006), arXiv:astro-ph/0512159 .
- N. Kaiser and M. J. Hudson, On the perturbation of the luminosity distance by peculiar motions, Mon. Not. Roy. Astron. Soc. 450, 883 (2015), arXiv:1411.6339 [astro-ph.CO] .
- R. A. Isaacson, Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics, Phys. Rev. 166, 1263 (1968).
- G. Cusin and M. Lagos, Gravitational wave propagation beyond geometric optics, Phys. Rev. D 101, 044041 (2020), arXiv:1910.13326 [gr-qc] .
- M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments, Oxford Master Series in Physics (Oxford University Press, 2007).
- P. Fleury, Light propagation in inhomogeneous and anisotropic cosmologies, Ph.D. thesis, Paris, Inst. Astrophys. (2015), arXiv:1511.03702 [gr-qc] .
- G. Cusin, C. Pitrou, and J.-P. Uzan, Are we living near the center of a local void?, JCAP 1703 (03), 038, arXiv:1609.02061 [astro-ph.CO] .
- A. Challinor, Microwave background polarization in cosmological models, Phys. Rev. D 62, 043004 (2000), arXiv:astro-ph/9911481 .
- C. G. Tsagas, A. Challinor, and R. Maartens, Relativistic cosmology and large-scale structure, Phys. Rept. 465, 61 (2008), arXiv:0705.4397 [astro-ph] .
- C. Pitrou, Radiative transport of relativistic species in cosmology, Astropart. Phys. 125, 102494 (2021), arXiv:1902.09456 [astro-ph.CO] .
- M. Boyle, Transformations of asymptotic gravitational-wave data, Phys. Rev. D 93, 084031 (2016), arXiv:1509.00862 [gr-qc] .
- A. Challinor and A. Lewis, Lensed CMB power spectra from all-sky correlation functions, Phys. Rev. D 71, 103010 (2005), arXiv:astro-ph/0502425 .
- G. Cusin, R. Durrer, and P. G. Ferreira, Polarization of a stochastic gravitational wave background through diffusion by massive structures, Phys. Rev. D 99, 023534 (2019), arXiv:1807.10620 [astro-ph.CO] .
- C. Pitrou, G. Cusin, and J.-P. Uzan, Unified view of anisotropies in the astrophysical gravitational-wave background, Phys. Rev. D 101, 081301 (2020), arXiv:1910.04645 [astro-ph.CO] .
- G. Cusin, C. Pitrou, and J.-P. Uzan, Anisotropy of the astrophysical gravitational wave background: Analytic expression of the angular power spectrum and correlation with cosmological observations, Phys. Rev. D96, 103019 (2017b), arXiv:1704.06184 [astro-ph.CO] .
- J. L. Synge, Relativity: The General Theory (1960).
- A. Torres-Orjuela, X. Chen, and P. Amaro Seoane, Excitation of gravitational wave modes by a center-of-mass velocity of the source, Phys. Rev. D 104, 123025 (2021).
- C. Pitrou, C. Bonvin, and G. Cusin, Peculiar velocity impact on reconstruction of parameters of a GW waveform,  in preparation .
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