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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
Abstract:
The Bondi-van der Burg-Metzner-Sachs (BMS) group, which uniquely describes
the symmetries of asymptotic infinity and therefore of the gravitational waves
that propagate there, has become increasingly important for accurate modeling
of waveforms. In particular, waveform models, such as post-Newtonian (PN)
expressions, numerical relativity (NR), and black hole perturbation theory,
produce results that are in different BMS frames. Consequently, to build a
model for the waveforms produced during the merging of compact objects, which
ideally would be a hybridization of PN, NR, and black hole perturbation theory,
one needs a fast and robust method for fixing the BMS freedoms. In this work,
we present the first means of fixing the entire BMS freedom of NR waveforms to
match the frame of either PN waveforms or black hole perturbation theory. We
achieve this by finding the BMS transformations that change certain charges in
a prescribed way -- e.g., finding the center-of-mass transformation that maps
the center-of-mass charge to a mean of zero. We find that this new method is 20
times faster, and more correct when mapping to the superrest frame, than
previous methods that relied on optimization algorithms. Furthermore, in the
course of developing this charge-based frame fixing method, we compute the PN
expression for the Moreschi supermomentum to 3PN order without spins and 2PN
order with spins. This Moreschi supermomentum is effectively equivalent to the
energy flux or the null memory contribution at future null infinity
$\mathscr{I}^{+}$. From this PN calculation, we also compute oscillatory
($m\not=0$ modes) and spin-dependent memory terms that have not been identified
previously or have been missing from strain expressions in the post-Newtonian
literature.
