Black Hole Formation and Space-Time Fluctuations in Two Dimensional Dilaton Gravity and Complementarity

TL;DR

This paper investigates black hole formation in a two-dimensional dilaton gravity model, revealing how boundary conditions influence horizon fluctuations and support the concept of black hole complementarity through quantum space-time fluctuations.

Contribution

It introduces the most general boundary conditions consistent with matter reflection, analyzes boundary dynamics at critical energy, and links quantum fluctuations to black hole complementarity.

Findings

Boundary recedes at light speed beyond critical energy

Large quantum fluctuations occur near the horizon for distant observers

Complementarity relates quantum effects to horizon fluctuations

Abstract

We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of the parameter which characterizes the boundary conditions, the boundary starts receeding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, an asymptotic observer using normal time resolutions will always measure large fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly the quantum gravity effects.