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Authors: Marc Favata (KITP)

Date: 30 Nov 2008

Abstract: The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasi-circular, inspiralling binaries, the Christodoulou memory produces a growing, non-oscillatory 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 non-oscillatory 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)-order. The memory is also potentially detectable in binary black hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasi-circular, 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 quasi-circular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory is essentially unchanged, the PN correction terms tend to reduce the memory's magnitude. Explicit expressions are given for the memory contributions to the polarizations and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the results of Blanchet et al. (2008), this completes the waveform to 3PN order. This paper also discusses: (i) difficulties in extracting the memory from numerical simulations, (ii) other non-oscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.

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