GW241011 data shows consistency with Kerr black holes for both quadrupole and octupole moments and delivers the first observational bounds on spin-induced octupole deviations.
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Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
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abstract
We introduce a formulation for spinning gravitating objects in the effective field theory in the post-Newtonian scheme in the context of the binary inspiral problem. We aim at an effective action, where all field modes below the orbital scale are integrated out. We spell out the relevant degrees of freedom, in particular the rotational ones, and the associated symmetries. Building on these symmetries, we introduce the minimal coupling part of the point particle action in terms of gauge rotational variables, and construct the spin-induced nonminimal couplings, where we obtain the leading order couplings to all orders in spin. We specify the gauge for the rotational variables, where the unphysical degrees of freedom are eliminated already from the Feynman rules, and all the orbital field modes are integrated out. The equations of motion of the spin can be directly obtained via a proper variation of the action, and Hamiltonians may be straightforwardly derived. We implement this effective field theory for spin to derive all spin dependent potentials up to next-to-leading order to quadratic level in spin, namely up to the third post-Newtonian order for rapidly rotating compact objects. In particular, the proper next-to-leading order spin-squared potential and Hamiltonian for generic compact objects are also derived. For the implementations we use the nonrelativistic gravitational field decomposition, which is found here to eliminate higher-loop Feynman diagrams also in spin dependent sectors, and facilitates derivations. This formulation for spin is thus ideal for treatment of higher order spin dependent sectors.
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representative citing papers
O(G^4) gravitational wave scattering amplitude computed in worldline QFT with Murua decomposition, matched to black hole perturbation theory to validate the formalism for Schwarzschild black holes.
The classical limit of five-dimensional spinning amplitudes reproduces the multipole expansion of five-dimensional black holes after augmenting with the Hodge dual of the spin tensor, and identifies amplitudes corresponding to the Myers-Perry solution.
Generalized Carter and Rüdiger constants for spinning charged probes in √Kerr backgrounds exist only for Wilson coefficients matching spin-exponentiated effective Compton amplitudes up to second order in spin.
A universal anomalous dimension for multipole moments in GR is derived via two EFT methods and applied to resum short-distance logarithmic tails in binary gravitational waveforms.
The NLO gravitational spin-orbit Hamiltonian for N spinning bodies is computed via PN-EFT, with only three-body diagrams new beyond the binary case, and the result matches the known ADM Hamiltonian up to canonical transformation.
Four relativistic spinning particle models (vector oscillator, spinor oscillator, spherical top, massive twistor) describe identical physics in free and interacting theories within the spin-magnitude-preserving sector.
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A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
NLO angular impulse for Kerr black holes computed to all orders in spin via KMOC formalism and leading singularities, with consistency checks and potential extraction.
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Testing the Kerr hypothesis beyond the quadrupole with GW241011
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Gravitational wave scattering at $\mathcal{O}(G^4)$: Murua construction and elliptics
O(G^4) gravitational wave scattering amplitude computed in worldline QFT with Murua decomposition, matched to black hole perturbation theory to validate the formalism for Schwarzschild black holes.
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Five-dimensional Geometry from Spinning Amplitudes
The classical limit of five-dimensional spinning amplitudes reproduces the multipole expansion of five-dimensional black holes after augmenting with the Hodge dual of the spin tensor, and identifies amplitudes corresponding to the Myers-Perry solution.
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Generalized Carter & R\"udiger Constants of $\sqrt{\text{Kerr}}$
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Resummation of Universal Tails in Gravitational Waveforms
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N-body next-to-leading order gravitational spin-orbit interaction via effective field theory
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Universality in Relativistic Spinning Particle Models
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