From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance

Abstract

In this paper we confirm the generalized actions of the complete NLO cubicin-spin interactions for generic compact objects which were tackled first via an extension of the EFT of spinning gravitating objects. The interaction potentials are made up of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, C ES 2 . We derived the full Hamiltonians in an arbitrary reference frame and in generic kinematic configurations. Using these most general Hamiltonians we find the full Poincaré algebra of all the sectors at the 4.5PN order, including the third subleading spin-orbit sector recently derived within our approach. We also derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we derive the extrapolated scattering angles in the aligned-spins case, and we find complete agreement with previous results derived for the scattering of black holes via scattering-amplitudes methods. The completion of the full Poincaré algebra at the 4.5PN order provides a strong validation that this new precision frontier in PN theory has now been established.

Scattering in black hole backgrounds and higher-spin amplitudes. Part II

“…In order to fully establish a correspondence between the spinning A n amplitudesor equivalent specifications of couplings in effective worldline theories in the PM [35][36][37][38][39][40][41] and post-Newtonian (PN) [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] approaches -and classical spinning BHs, matching computations that go beyond the stationary limit need to be done. A first step has been taken along these lines by the authors of [60], where, up to the third order in the BH's spin, results for the 2PM aligned spin scattering angle -computed in [6] from the minimal coupling A 3 and A 4 -were shown to be consistent with the general-relativistic "self-force" calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body [61,62]; in particular, the gravitational observables, Detweiler redshift [63], and the circular orbit precession frequency were considered for the matching computation in [60].…”

Poincaré invariance of spinning binary dynamics in the post-Minkowskian Hamiltonian approach

“…in [12][13][14][15]. Recently, the construction was completed up to the overwhelming 5PN order in [16,17].…”

Spin supplementary condition in quantum field theory: covariant SSC and physical state projection

“…The observations of gravitational waves from compact binary coalescence [4,5] have necessitated a better understanding of compact binary dynamics, attracting practitioners of quantum field theory (QFT) to develop QFT-inspired methods for handling the relativistic two-body problem . An important aspect of relativistic two-body dynamics is the effects of spin, where QFT-inspired methods have proved to be powerful tools for their understanding, as can be inferred from the vast number of recent works on the subject; post-Newtonian effective field theory (PNEFT) [49][50][51][52][53][54][55][56][57][58][59], scattering amplitudes [1,2,[60][61][62][63][64][65][66][67][68][69][70][71][72], post-Minkowskian effective field theory [73], and worldline quantum field theory (WQFT) [74][75][76][77][78]. Of course, each approach comes with its own shortcomings; e.g.…”