Energy map and effective metric in an effective-one-body theory based on the second-post-Minkowskian approximation

Abstract

Effective-one-body (EOB) theory was originally proposed based on the post-Newtonian (PN) approximation and plays an important role in the analysis of gravitational wave signals. Recently, the post-Minkowskian (PM) approximation has been applied to the EOB theory. The energy map and the effective metric are the two key building blocks of the EOB theory, and in PN approximation radial action variable correspondence is employed to construct the energy map and the effective metric. In this paper, we employ the PM approximation up to the second order, and use the radial action variable correspondence and the precession angle correspondence to construct the energy map and the effective metric. We find that our results based on the radial action variable correspondence, are exactly the same with those obtained based on the precession angle correspondence. Furthermore, we compare the results obtained in this work to the previous existing ones.

Waveforms from Amplitudes

“…Finally, two of the present authors have examined light-ray operators [104] and shock waves [105]. Researchers working within a traditional GR framework have also continued to produce new results [106][107][108][109][110][111][112][113][114][115][116][117][118][119][120].…”

The Gravitational-wave physics II: Progress

“…The EOB approach describes the conservative dynamics of the two-body problem in GR as a geodesic motion (more precisely Mathisson-Papapetrou-Dixon equation [794]) on the top of an effective spacetime of the reduced one body. The Finsler-type term may possibly be involved besides the geodesic motion [795,796]. The reduced one body spacetime is a deformed Kerr black hole [797].…”

The Gravitational-Wave Physics II: Progress

“…The basic idea of the EOB approach is describing the conservative dynamics of the two-body problem in GR as a geodesic motion (more precisely Mathisson-Papapetrou-Dixon equation [753]) on the top of an effective spacetime which corresponds to the reduced one body. The Finsler-type term may possibly be involved besides the geodesic motion [754,755]. Roughly the reduced spacetime is a deformed Kerr black hole with metric form [756].…”

“…Corresponding to the geodesic motion, the Hamiltonian can be written as [747,755,757] Since the part 2 is related to the part 3, we describe our waveform formula first, and introduce the back reaction force afterwards. The gravitational waveform is described by spin-weighted −2 spherical harmonic modes.…”