Compton Amplitude for Rotating Black Hole from QFT

We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian potential induced by massless conformal matter for spinless particles are well-known, and the same corrections due to massless minimally coupled scalars [Class. Quant. Grav. 27 (2010) 245008], massless non-conformal scalars [Phys. Rev. D 87 ...

It has been shown that a special set of three-point amplitudes between two massive spinning states and a graviton reproduces the linearised stress-energy tensor for a Kerr black hole in the classical limit. In this work we revisit this result and compare it to the analysis of the amplitudes describing the interaction of leading Regge states of the open and closed superstring. We find an all-spin result for the classical limit of two massive spinning states interacting with a ...

Quantum amplitudes for $s=1$ at Maxwell fields and for $s=2$ linearised gravitational wave perturbations of a spherically symmetric Einstein/massless scalar background, describing gravitational collapse to a black hole, are treated by analogy with a previous treatment of $s=0$ scalar-field perturbations of gravitational collapse at late times. In both the $s=1$ and $s=2$ cases, we isolate suitable 'co-ordinate' variables which can be taken as boundary data on a final space-li...

We study the compatibility of recursive techniques with the classical limit of scattering amplitudes through the construction of the classical Compton amplitude for general spinning compact objects. This is done using BCFW recursion on three-point amplitudes expressed in terms of the classical spin vector and tensor, and expanded to next-to-leading-order in $\hbar$ by using the heavy on-shell spinors. Matching to the result of classical computations, we find that lower-point ...

It has recently been pointed out that particles falling freely from rest at infinity outside a Kerr black hole can in principle collide with arbitrarily high center of mass energy in the limiting case of maximal black hole spin. Here we aim to elucidate the mechanism for this fascinating result, and to point out its practical limitations, which imply that ultra-energetic collisions cannot occur near black holes in nature.

This work on spin-0 amplitudes in black-hole evaporation is based on the underlying results and methods outlined in our first paper, "I. Complex Approach". The main result here, and the model calculation for work on all higher spins, as described in several further papers, is the computation of the quantum amplitude (rather than merely the probability) for a given slightly anisotropic configuration of a scalar field $\phi$ on a space-like hypersurface $\Sigma_F$ at a very lat...

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...

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime $M\mu\gg1$ (here $M$ and $\mu$ are respectively the mass of the central black hole and the proper ...

We discuss the dRGT massive gravity interacting with spin-0, spin-1/2, or spin-1 matter. The effective theory of a massive spin-2 particle coupled to matter particles is constructed directly at the amplitude level. In this setting we calculate the gravitational Compton scattering amplitudes and study their UV properties. While the Compton amplitudes generically grow with energy as $\mathcal{O}(E^6)$, we identify regions of the parameter space where they are softened to $\math...

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...