Scattering of gravitational waves off spinning compact objects with an effective worldline theory

Abstract

We study the process, within classical general relativity, in which an incident gravitational plane wave, of weak amplitude and long wavelength, scatters off a massive spinning compact object, such as a black hole or neutron star. The amplitude of the asymptotic scattered wave, considered here at linear order in Newton's constant $G$ while at higher orders in the object's multipole expansion, is a valuable characterization of the response of the object to external gravitational fields. This amplitude coincides with a classical ($\hslash \to 0$) limit of a quantum 4-point (object and graviton in, object and graviton out) gravitational Compton amplitude, at the tree (linear-in-$G$) level. Such tree-level Compton amplitudes are key building blocks in generalized-unitary-based approaches to the post-Minkowskian dynamics of binaries of spinning compact objects. In this paper, we compute the classical amplitude using an effective worldline theory to describe the compact object, determined by an action functional for translational and rotational degrees of freedom, including couplings of spin-induced higher multipole moments to spacetime curvature. We work here up to the levels of quadratic-in-spin quadrupole and cubic-in-spin octupole couplings, respectively involving Wilson coefficients $C_2$ and $C_3$. For the special case $C_2=C_3=1$ corresponding to a black hole, we find agreement through cubic-in-spin order between our classical amplitude and previous conjectures arising from considerations of quantum scattering amplitudes. We also present new results for general $C_2$ and $C_3$, anticipating instructive comparisons with results from effective quantum theories.

v2: minor corrections and additional discussion; two-column format; submitted to PRD

References in corpus (15)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Gravitational spin Hamiltonians from the S matrix
• Scattering and absorption of gravitational plane waves by rotating black holes
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• From Boundary Data to Bound States III: Radiative Effects
• Improved next-to-leading order tidal heating and torquing of a Kerr black hole
• Scattering of Long-Wavelength Gravitational Waves
• Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
• Gravitons scattering from classical matter

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• Bethe-Salpeter equation for classical gravitational bound states
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Investigating tidal heating in neutron stars via gravitational Raman scattering
• Classical off-shell currents
• Quasinormal modes of slowly-spinning horizonless compact objects
• Charged test-particle scattering and effective one-body metrics with spin
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT