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arXiv · 2506.09946

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

Voja Radovanović·Stefan Đorđević
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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.

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Voja Radovanović, Stefan Đorđević. 2025-06-11. Collapse Scenario and Final State of Evaporation for Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity. https://arxiv.org/abs/2506.09946

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