Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

115

We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $$ \mathcal{O} $$ O (G2) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in [1] that relates the impulse and spin kick in a scattering event to the eikonal phase.

Section: Acknowledgmentsmentioning

confidence: 95%

“…Note added. As this paper was in its latest stages we learned about [117], which contains overlap with our work. Ref.…”

Section: Jhep07(2021)037mentioning

confidence: 99%

See 1 more Smart Citation

Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

Kosmopoulos¹,

Luna²

2021

115

“…Recent years have seen a number of applications of onshell techniques, pioneered in Quantum Field Theory, to the classical general relativistic two-body problem. Notable examples include generalized unitarity [25][26][27], the double copy [28][29][30][31][32][33], and effective field theory ideas [34][35][36] that have produced new results for the dynamics of spinless [10,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] and spinning [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] black holes, including finite-size effects [68][69][70]…”

Section: Introductionmentioning

confidence: 99%

Radiative classical gravitational observables at $$ \mathcal{O} $$(G3) from scattering amplitudes

Herrmann¹,

Parra-Martinez

Ruf

et al. 2021

166

137

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and $$ \mathcal{N} $$ N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $$ \mathcal{O} $$ O (G3) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

“…A new perspective on JHEP10(2021)008 this classical problem in general relativity has recently been offered by methods rooted in quantum field theory (QFT), which profit from a wide variety of on-shell methods developed for the study of quantum scattering amplitudes. In particular, many state-of-the-art post-Minkowskian (PM) computations of the two-body dynamics of Schwarzschild and Kerr black holes have been performed using the philosophy of effective field theory (EFT), either in the genuinely quantum-theoretic sense [3][4][5][6][7][8] or in the form of classical worldline effective theory [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], see also refs. [25][26][27][28][29][30][31][32] for concurrent developments using eikonal methods.…”

Section: Introductionmentioning

confidence: 99%

Classical observables from coherent-spin amplitudes

Aoude

Ochirov

2021

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O’Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group SU(2) and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton’s constant.