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-shell leading-singularity method and using massive spinorhelicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion. arXiv:1812.06895v3 [hep-th] 9 Sep 2019 Contents 1 Introduction 1 2 Multipole expansion of three-and four-point amplitudes 6 3 Scattering angle as Leading Singularity 17 4 Discussion 27 A Three-point amplitude with spin-1 matter 29 B Spin tensor for spin-1 matter 30 C Angular-momentum operator 32Recently, a classical version of the soft theorem up to sub-subleading order has been used by Laddha and Sen [22] to derive the spectrum of the radiated power in black-hole scattering with external soft graviton insertions. This relies on the remarkable fact that conservative and non-conservative long-range effects of interacting black holes can be computed from the scattering of massive point-like sources [23][24][25][26]. Indeed, rotating black holes can be treated via a spin-multipole expansion, the order 2s of which can be reproduced by scattering spins minimally coupled particles exchanging gravitons [27], as illustrated in figure 1a. The matching between these amplitudes with spin and a non-relativistic potential for black-hole scattering has been performed explicitly in the post-Newtonian (PN) framework [27][28][29].Here we present a complementary picture to the one of [22] by employing the soft theorem in the conservative sector (i.e. no external gravitons), focusing on rotating black holes and at the same time extending the soft factor in (1.1) to higher orders in the soft expansion. This is achieved in the following way: It was shown by one of the authors in [29] that the classical ( -independent) piece of the spin-s amplitude can be extracted from a covariant Holomorphic Classical...

The gravitational wave signal from an inspiralling binary neutron star system will contain detailed information about tidal coupling in the system, and thus, about the internal physics of the neutron stars. To extract this information will require highly accurate models for the gravitational waveform. We present here a calculation of the gravitational wave signal from a binary with quadrupolar tidal interactions which includes all post-1-Newtonian-order effects in both the conservative dynamics and wave generation. We consider stars with adiabatically induced quadrupoles moving in circular orbits, and work to linear order in the stars' quadrupole moments. We find that post-1-Newtonian corrections increase the tidal signal by approximately 20% at gravitational wave frequencies of 400 Hz.

We demonstrate equivalences, under simple mappings, between the dynamics of three distinct systems-(i) an arbitrary-mass-ratio two-spinning-black-hole system, (ii) a spinning test black hole in a background Kerr spacetime, and (iii) geodesic motion in Kerr-when each is considered in the first post-Minkowskian (1PM) approximation to general relativity, i.e. to linear order G but to all orders in 1/c, and to all orders in the black holes' spins, with all orders in the multipole expansions of their linearized gravitational fields. This is accomplished via computations of the net results of weak gravitational scattering encounters between two spinning black holes, namely the net O(G) changes in the holes' momenta and spins as functions of the incoming state. The results are given in remarkably simple closed forms, found by solving effective Mathisson-Papapetrou-Dixon-type equations of motion for a spinning black hole in conjunction with the linearized Einstein equation, with appropriate matching to the Kerr solution. The scattering results fully encode the gaugeinvariant content of a canonical Hamiltonian governing binary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbits and spin orientations. We deduce one such Hamiltonian, which reproduces and resums the 1PM parts of all such previous post-Newtonian results, and which directly manifests the equivalences with the test-body limits via simple effective-one-body mappings.

We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.

We study the link between classical scattering of spinning black holes and quantum amplitudes for massive spin-s particles. Generic spin orientations of the black holes are considered, allowing their spins to be deflected on par with their momenta. We re-derive the spin-exponentiated structure of the relevant tree-level amplitude from minimal coupling to Einstein's gravity, which in the s → ∞ limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function is seen to encode in a simple way the known net changes in the black-hole momenta and spins at first post-Minkowskian order. We connect our findings to a rigorous framework developed elsewhere for computing such observables from amplitudes. 1 We note that Refs. [10,31,32] have also treated spin contributions at 2PM order, and that Ref.[33] has also considered radiative effects via a classical double copy with spin.