2008/12/31 by M. Favata, Marc Favata · 184 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #General relativity #Gravitation #Gravitational wave #Numerical relativity #Physics #Polarization (electrochemistry) #Pulsars and Gravitational Waves Research #astro-ph.SR #gr-qc
paper · pdf · doi:10.1103/physrevd.80.024002
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 80(2) (American Physical Society) · 25 pages, 6 figures; v2: 27 pages, expanded discussion and presentation, corrected typos, main results unchanged. Matches published PRD version
arxiv created 2009/06/21 · openalex publication_date 2009/07/02 · arxiv updated 2010/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasicircular, inspiralling binaries, the Christodoulou memory produces a growing, nonoscillatory change in the gravitational-wave ``plus'' polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its nonoscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading (Newtonian/quadrupole) order. The memory is also potentially detectable in binary black-hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasicircular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasicircular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory remains qualitatively unchanged, the PN correction terms tend to reduce the memory's magnitude. Explicit expressions are given for the memory contributions to the plus polarization and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the recent results of Blanchet et al. [Classical Quantum Gravity 25, 165003 (2008)], this completes the waveform polarizations to 3PN order. This paper also discusses: (i) the difficulties in extracting the memory from numerical relativity simulations, (ii) other nonoscillatory effects that enter the waveform polarizations at high PN orders, and (iii) issues concerning the observability of the memory in gravitational-wave detectors.