The Black Hole S-Matrix from Quantum Mechanics

TL;DR

This paper reformulates the black hole S-Matrix using quantum mechanics, specifically inverted harmonic oscillators, revealing a connection to 2D string theory and an exponential degeneracy in energy distribution among partial waves.

Contribution

It introduces a quantum mechanical model of scattering that reproduces the black hole S-Matrix and links it to 2D string theory, highlighting degeneracy in energy distribution.

Findings

Reproduces the unitary black hole S-Matrix for all partial waves.

Establishes a connection between black hole scattering and 2D string theory.

Shows exponential degeneracy in energy distribution among partial waves.

Abstract

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 harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.