Semiclassical S-matrix and black hole entropy in dilaton gravity

TL;DR

This paper employs a semiclassical approach to analyze particle scattering in dilaton gravity with a boundary, revealing a connection between scattering suppression at high energies and black hole entropy, consistent with thermodynamic principles.

Contribution

It introduces a semiclassical method to compute scattering amplitudes in dilaton gravity, linking scattering suppression to black hole entropy and fixing the entropy's constant term.

Findings

Below critical mass, scattering is trivial with unit probability.

At energies above critical mass, scattering amplitude is exponentially suppressed.

Derived an expression for black hole entropy consistent with thermodynamics.

Abstract

We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass $M_{cr}$. We find that at energies below $M_{cr}$ the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate black hole decaying into the final-state particle. Relating the suppression of the scattering probability to the number of the intermediate black hole states, we find an expression for the black hole entropy consistent with thermodynamics. In addition, we fix the constant part of the entropy which is left free by the thermodynamic arguments. We rederive this result by modifying the standard Euclidean entropy calculation.