On 't Hooft's S-matrix Ansatz for quantum black holes

TL;DR

This paper explores 't Hooft's S-matrix approach to quantum black holes, analyzing gravitational effects, operator algebra, and analogies with other physical systems to address quantum gravity challenges.

Contribution

It revisits and extends 't Hooft's S-matrix framework, examining backreaction, operator exchange algebras, and potential methods for incorporating nonlinear gravity effects.

Findings

Gravitational backreaction affects Hawking radiation properties.

Exchange algebras relate ingoing and outgoing matter operators.

Higher order derivatives may aid in black hole microstate counting.

Abstract

The S-matrix Ansatz has been proposed by 't Hooft to overcome difficulties and apparent contradictions of standard quantum field theory close to the black hole horizon. In this paper we revisit and explore some of its aspects. We start by computing gravitational backreaction effects on the properties of the Hawking radiation and explain why a more powerful formalism is needed to encode them. We then use the map bulk-boundary fields to investigate the nature of exchange algebras satisfied by operators associated with ingoing and outgoing matter. We propose and comment on some analogies between the non covariant form of the S-matrix amplitude and liquid droplet physics to end up with similarities with string theory amplitudes via an electrostatic analogy. We finally recall the difficulties that one encounters when trying to incorporate non linear gravity effects in 't Hooft's S-matrix and observe how the inclusion of higher order derivatives might help in the black hole microstate counting.