Compton Amplitude for Rotating Black Hole from QFT

We propose a candidate Compton amplitude which is valid for any (integer) quantum spin and free from any spurious poles. We consider the cases of electromagnetism and gravity. We obtain such amplitudes by calculating the corresponding ones from superstring theory involving states on the leading Regge trajectory. To extract the associated field-theory amplitudes a few considerations in the form of simple physical constraints are required, such as: Soft momentum transfer, compa...

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....

We present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the \textit{confluent Heun equation} (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase-shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) pertu...

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...

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...

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...

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...

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 study the EFT of a spinning compact object and show that with appropriate gauge fixing, computations become amenable to worldline quantum field theory techniques. We use the resulting action to compute Compton and one-loop scattering amplitudes at fourth order in spin. By matching these amplitdes to solutions of the Teukolsky equations, we fix the values of Wilson coefficients appearing in the EFT such that it reproduces Kerr black hole scattering. We keep track of the spi...