Abstract
Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes.
Highlights
The demonstrated feasibility of direct detection of gravitational waves (GWs) from binary systems [1,2], and, in particular, the observation of neutron star inspirals [3], has revealed a new window to explore compact objects in an unprecedented fashion [4,5,6]
We reconstruct a Hamiltonian incorporating tidal effects to next-to-leading order (NLO) in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes
Do GWs carry the imprint of the equation of state of nuclear matter through tidal effects [7,8,9], but they have opened new frontiers for beyond the standard model searches [10,11,12], as well as the exploration of the remarkable properties of black holes in Einstein’s gravity [5,6]
Summary
The demonstrated feasibility of direct detection of gravitational waves (GWs) from binary systems [1,2], and, in particular, the observation of neutron star inspirals [3], has revealed a new window to explore compact objects in an unprecedented fashion [4,5,6]. Partially due to the repurposing of powerful tools from the amplitudes program, e.g., [49,50,51,52,53,54,55,56,57,58], as well as EFT, e.g., [49,50], the boundary-to-bound dictionary [59,60] and other developments, e.g., [61,62,63,64,65], it has become apparent that the study of scattering in the post-Minkowskian (PM) expansion may push further the frontiers of analytic understanding of binary systems With these ideas at hand, a worldline EFT approach was developed in [66] and readily implemented in [67] to reach the present state-of-the-art at 3PM [52,53,56]. Unlike the derivations in [52,53,56,69], ours is reduced to (massless) integrals, whose velocity dependence can be obtained via differential equation from the EFT with static classical sources [67], which greatly simplifies the calculations
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