High-Energy Gravitational Scattering and Bose-Einstein Condensates of Gravitons

TL;DR

This paper connects high-energy gravitational scattering with the concept of black holes as Bose-Einstein condensates of gravitons, providing a new framework to understand quantum black holes through scattering amplitudes and condensate properties.

Contribution

It establishes a link between scattering amplitudes and graviton condensate models of black holes, including calculations of corrections and implications for quantum black hole probes.

Findings

Scattering amplitude dominated by N graviton exchange follows a Poisson distribution.

Supports the view of black holes as graviton Bose-Einstein condensates with size related to the Schwarzschild radius.

Provides a method to compute 1/N corrections from fluctuations around saddle points.

Abstract

Quantum black holes are difficult to describe. We consider two seemingly divergent approaches, high-energy scattering and the proposal to regard black holes as Bose-Einstein condensates of gravitons, and establish a connection between them. High-energy scattering is studied in the eikonal approximation, which is processed further by a saddle-point approximation. The dominant contribution to the scattering amplitude comes from a ladder diagram with the exchange of N gravitons, and the number of gravitons follows a Poisson distribution. This approximation supports the picture of a graviton Bose-Einstein condensate with an extent equal the Schwarzschild radius, which grows with N in a way determined by the saddle point. The approach permits calculations of 1 / N corrections from the fluctuations around the saddle points and we comment on these. Scattering methods might be useful probes of quantum black holes, especially when interpreted in terms of condensates.