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Collapse scenario and final state of evaporation for Schwarzschild black hole in dimensionally reduced model of dilaton gravity

Stefan Đorđević and Voja Radovanović

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Phys. Rev. D 113, 105010 – Published 14 May, 2026

DOI: https://doi.org/10.1103/q2n7-qnc1

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 backreaction. 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. Along this hypersurface, the metric can be continuously matched to a static end-state geometry. This end-state geometry is a quantum-corrected Minkowski space-time within the first order of perturbation theory.

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Phys. Rev. D 113, 105010– Published 14 May, 2026
  • Received 13 June 2025
  • Accepted 24 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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