Collapse Scenario and Final State of Evaporation for Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity

TL;DR

This paper investigates the evaporation process of Schwarzschild black holes within a (1+1)-dimensional dilaton gravity model, revealing the horizon's shrinkage, singularity encounter, and transition to a Minkowski end-state.

Contribution

It provides a perturbative analysis of black hole evaporation in a dimensionally-reduced model, including back-reaction effects and the matching of the evolving geometry to a static end-state.

Findings

Black hole horizons shrink and meet the singularity during evaporation.

A shockwave forms at the point where the horizon meets the singularity.

The end-state geometry after evaporation is Minkowski space-time.

Abstract

We study a model of (1+1)-dimensional dilaton gravity derived from the four-dimensional Einstein-Hilbert action by dimensional reduction in a semiclassical approximation including back-reaction. The reduced action involves the cosmological constant and admits black hole solutions; among these, the solutions of interest are the evaporating black holes. We solve the equations of motion perturbatively by demanding that the initial state geometry is a Minkowski space-time. When the infalling matter intersects the space-time boundary, the black hole forms and begins to evaporate. We find that as the black hole evaporates, its horizon shrinks and at a finite space-time point, it meets the singularity and a shockwave occurs. Along this hypersurface, the metric can be continuously matched to a static end-state geometry. This end-state geometry is Minkowski space-time within the first-order of perturbation theory.