Dynamics of Spinning Binary at 2PM

Using the recently derived higher spin gravitational Compton amplitude from low-energy analytically continued ($a/Gm\gg1$) solutions of the Teukolsky equation for the scattering of a gravitational wave off the Kerr black hole, observables for non-radiating super-extremal Kerr binary systems at second post-Minkowskian (PM) order and up to sixth order in spin are computed. The relevant 2PM amplitude is obtained from the triangle-leading singularity in conjunction with a general...

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 ...

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...

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-Ke...

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal pha...

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 ...

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...

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...

Accurate modeling of compact binaries is essential for gravitational-wave detection and parameter estimation, with spin being an important effect to include in waveform models. In this paper, we derive new post-Newtonian (PN) results for the conservative aligned-spin dynamics at next-to-next-to-leading order for the spin$^3$ and spin$^4$ contributions, in addition to the next-to-leading order (NLO) spin$^5$ and spin$^6$ contributions. One approach we follow is the Tutti Frutt...

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through $\mathcal{O}(G^3)$ to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numer...