Dynamics of Spinning Binary at 2PM

We study the binary dynamics of two Kerr black holes with arbitrary spin vectors in the presence of parity-even and parity-odd cubic deformations of gravity. We first derive the tree-level Compton amplitudes for a Kerr black hole in cubic gravity, which we then use to compute the two-to-two amplitudes of the massive bodies to leading order in the deformation and the post-Minkowskian expansion. The required one-loop computations are performed using the leading singularity appr...

We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to $S^2 = -s(s+1)\hbar^2$, using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin...

Previously the linearized stress tensor of a stationary Kerr black hole has been used to determine some of the values of gravitational couplings for a spinning black hole to linear order in the Riemann tensor in the action (worldline or quantum field theory). In particular, the couplings on operators containing derivative structures of the form $(S\cdot\nabla)^n$ acting on the Riemann tensor were fixed, with $S^\mu$ the spin vector of the black hole. In this paper we find tha...

We present a calculation of the conservative two-body Hamiltonian of a compact binary system including a spinning black hole. We include up-to third order corrections in Newton's constant $G$, all orders in velocity, and linear and quadratic terms in spin. The results are obtained from the classical limit of two-loop scattering amplitudes involving two massive scalars and two massive spin-1 particles minimally coupled to gravity. We discuss the usage of numerical techniques i...

In this paper we study the two-body gravitational scattering of massive scalars with different masses in general spacetime dimensions. We focus on the Regge limit (eikonal regime) of the resulting scattering amplitudes and discuss how to extract the classical information representing the scattering of two black holes. We derive the leading eikonal and explicitly show the resummation of the first leading energy contribution up to second order in Newton's gravitational constant...

We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably-chosen effective field theory, we obtain the spin1-spin2 terms of a two-body effective Hamiltonian through O(...

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...

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...

We present a new approach to solve the 2+1 Teukolsky equation for gravitational perturbations of a Kerr black hole. Our approach relies on a new horizon penetrating, hyperboloidal foliation of Kerr spacetime and spatial compactification. In particular, we present a framework for waveform generation from point-particle perturbations. Extensive tests of a time domain implementation in the code {\it Teukode} are presented. The code can efficiently deliver waveforms at future nul...

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name "classical spin covariant derivative", that is compatible with the three-point interaction of the $\sqrt{\mathrm{Kerr}}$ solution with the gauge field. The resulting Lagrangian, beside the correct three-point coupling, predicts a unique choice for contact terms and ther...