Scattering in Black Hole Backgrounds and Higher-Spin Amplitudes: Part II

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 calculate the scattering of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at $\mathcal{O}(G^2)$ and all orders in the spins of both objects. This is done including the complete set of contact terms potentially relevant to Kerr-black-hole scattering at $\mathcal{O}(G^2)$. As such, Kerr black holes should be described by this scattering amplitude for a specific choice of values for the contact-term coefficients. The inclusion o...

We consider the covariant proposal for the gravitational Compton amplitude for a Kerr black hole. Employing the covariant three- and four-point Compton amplitudes, we assemble the classical one-loop integrand on the maximal cut at all orders in spin, utilizing the method of unitarity. Expanding in powers of spin, we evaluate the one-loop amplitude up to $\mathcal O(G^2 a^8)$. Supplemented with extra contact contributions derived from the far-zone data of the Teukolsky solutio...

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 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 rederive the spin-exponentiated structure of the relevant tree-level amplitude from minimal coupling to Einstein's gravity, which in the $s\to\infty$ limit generates the black holes' complete series of spin-induced multipoles....

Quantum higher-spin theory applied to Compton amplitudes has proven to be surprisingly useful for elucidating Kerr black hole dynamics. Here we apply the framework to compute scattering amplitudes and observables for a binary system of two rotating black holes, at second post-Minkowskian order, and to all orders in the spin-multipole expansion for certain quantities. Starting from the established three-point and conjectured Compton quantum amplitudes, the infinite-spin limit ...

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 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...

In this thesis we present a study of the computation of classical observables in gauge theories and gravity directly from scattering amplitudes. In particular, we discuss the direct application of modern amplitude techniques in the one, and two-body problems for both, scattering and bounded scenarios, and in both, classical electrodynamics and gravity, with particular emphasis on spin effects in general, and in four spacetime dimensions. Among these observables we have the co...

We study the process, within classical general relativity, in which an incident gravitational plane wave, of weak amplitude and long wavelength, scatters off a massive spinning compact object, such as a black hole or neutron star. The amplitude of the asymptotic scattered wave, considered here at linear order in Newton's constant $G$ while at higher orders in the object's multipole expansion, is a valuable characterization of the response of the object to external gravitation...