The simplest massive S-matrix: from minimal coupling to Black Holes

As shown recently 2d quantum gravity theories -- including spherically reduced Einstein-gravity -- after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as...

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...

Recent studies have shown that minimal couplings for massive spinning particles, which in the classical limit reproduce the leading PM Kerr black hole dynamics, leads to an Eikonal S-matrix exhibiting spin-entanglement suppression. In this paper we trace this phenomenon to the suppression of spin-flipping components in the S-matrix, known to be the hallmark of minimal coupling in the ultra-relativistic limit. We further generalize the consideration to charged and $\mathcal{N}...

A non-trivial $\mathcal{S}$-matrix generally implies a production of entanglement: starting with an incoming pure state the scattering generally returns an outgoing state with non-vanishing entanglement entropy. It is then interesting to ask if there exists a non-trivial $\mathcal{S}$-matrix that generates no entanglement. In this letter, we argue that the answer is the scattering of classical black holes. We study the spin-entanglement in the scattering of arbitrary spinning...

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic am...

We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniqu...

We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory & $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\textemdash of waves scattering off inverted harmonic oscillator potentials\textemdash that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmoni...

Free massive higher spin fields in weak background gravitational fields are discussed. Contrary to the spin one case, higher spin fields should have nontrivial non-minimal couplings to the curvature. A precise analysis is given for the spin 2 case, and it is shown that two conditions should be satisfied among five non-minimal coupling constants, which we derive both in the Hamiltonian and Lagrangian formalisms. It is checked that the linearized limit of the massive gravity th...

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 review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to lead...