December 15, 2022
We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole's spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical ($a/GM<1$) to a particle-like ($a/GM>1$) regime. Up to the sixth order in spin, we identify a unique \textit{conservative} part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes.
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July 21, 2021
The scattering of massless waves of helicity $|h|=0,\frac{1}{2},1$ in Schwarzschild and Kerr backgrounds is revisited in the long-wavelenght regime. Using a novel description of such backgrounds in terms of gravitating massive particles, we compute classical wave scattering in terms of $2\to 2$ QFT amplitudes in flat space, to all orders in spin. The results are Newman-Penrose amplitudes which are in direct correspondence with solutions of the Regge-Wheeler/Teukolsky equation...
July 30, 2021
Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitational-wave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higher-spin amplitudes ...
September 16, 2019
It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant $G$, that the classical aligned-spin scattering function for an arbitrary-ma...
December 17, 2018
We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on...
June 19, 2024
We study the $2 \to 2$ scattering in the regime where the wavelength of the scattered objects is comparable to their distance but is much larger than any Compton wavelength in the quantum field theory. We observe that in this regime - which differs from the eikonal - the Feynman diagram expansion takes the form of a geometric series, akin to the Born series of quantum mechanics. Conversely, we can define the Feynman diagram expansion as the Born series of a relativistic effec...
May 5, 2022
Making use of the recently-derived, all-spin, opposite-helicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at $\mathcal{O}(G^{2})$ and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with ...
October 6, 2023
We compute the classical tree-level five-point amplitude for the two-to-two scattering of spinning celestial objects with the emission of a graviton. Using this five-point amplitude, we then turn to the computation of the leading-order time-domain gravitational waveform. The method we describe is suitable for arbitrary values of classical spin of Kerr black holes and does not require any expansion in powers of the spin. In this paper we illustrate it in the simpler case of th...
March 11, 2022
The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point amplitudes of ref. \cite{Arkani-Hamed:2017jhn}) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose cont...
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We develop a novel amplitude bootstrap technique manifestly free of unphysical poles for classically spinning particles interacting with gravitons utilizing only the gauge/gravity double-copy and physical factorization limits. Combined with non-factorization polynomial contact contributions from physical data for Kerr black holes, we can address high-spin-order covariant gravitational Compton amplitudes, identifying a pattern for the amplitude that we believe could extend to ...
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We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin $s=0,1/2,1,\dots, \infty$, from which we extract the corresponding classical amplitude to all orders in the spin vector $S^\mu$. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of f...