Scattering of tidally interacting bodies in post-Minkowskian gravity

Abstract

The post-Minkowskian approach to gravitationally interacting binary systems (i.e., perturbation theory in G, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the first post-Minkowskian order. The corresponding contributions to the scattering angle are derived.

Horizon radiation reaction forces

“…In particular, we have extended our results in [11], where only the time averaged dissipation was discussed. 7 These results complement the calculations in [35,51] for the PM scattering angle resulting from conservative finite size effects. In order to treat dissipation in the case of more general compact objects, the only modifications needed to the calculations presented in this paper are the retarded correlators which we define in eqs.…”

“…(3.20) can also be used to calculate dissipative effects in PM scattering. A quantity that has received attention in the recent literature [25,27,28,30,34,35], due to its connection with the EOB framework [36,37]…”

“…This is partly motivated by recent developements connecting classical PM scattering in general relativity (see e.g. [22][23][24][25][26][27][28][29][30][31][32][33][34][35]), the Effective One Body (EOB) [36,37] approach used to model the intermediate stages of the binary inspiral, and modern scattering amplitude approaches to classical gravitational scattering, see e.g. [38][39][40][41][42][43][44][45][46][47][48][49][50][51].…”

“…The inelastic PM corrections we obtain are not easily accessible to scattering amplitude methods (based on an underlying unitary S-matrix description of point particles) and it would be interesting to incorporate our results in section 3.1 into the EOB formalism, as has been recently discussed in refs. [25,27,28,30,34,35] in the context of elastic scattering.…”

Second-order post-Minkowskian scattering in arbitrary dimensions

“…Given the expected improvements in detector sensitivity, it will be extremely important in the future to have high-precision theoretical predictions from General Relativity. To this aim the use of quantum field theory amplitudes to extract the post-Minkowskian (PM) expansion of General Relativity has recently gained considerable momentum [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and progress is now also being made on extensions to spinning objects [22][23][24][25][26][27][28][29][30][31]. The underlying physical motivation for this approach lies in the observation that, during the early stages of a merger event, when the two compact objects are still far apart, gravitational interactions are weak and can be conveniently treated JHEP07(2020)122 in a weak-coupling approximation.…”