An Analytic Description of Semi-Classical Black-Hole Geometry

Abstract

We study analytically the spacetime geometry of the black-hole formation and evaporation. As a simplest model of the collapse, we consider a spherical thin shell, and take the back-reaction from the negative energy of the quantum vacuum state. For definiteness, we will focus on quantum effects of s-waves. We obtain an analytic solution of the semi-classical Einstein equation for this model, that provides an overall description of the black hole geometry form the formation to evaporation. As an application of this result, we find its interesting implication that, after the collapsing shell enters the apparent horizon, the proper distance between the shell and the horizon remains as small as the Planck length even when the difference in their areal radii is of the same order as the Schwarzschild radius. The position of the shell would be regarded as the same place to the apparent horizon in the semi-classical regime of gravity.

arXiv comment42 pages, 8 figures, minor modification

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Cited by in corpus (12)

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• Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation
• UV And IR Effects On Hawking Radiation
• Entanglement entropy and vacuum states in Schwarzschild geometry
• From Uneventful Horizon to Firewall in D-Dimensional Effective Theory
• Firewall From Effective Field Theory
• Unveiling horizons in quantum critical collapse
• Distance between collapsing matter and trapping horizon in evaporating black holes
• Quantum Critical Collapse Abhors a Naked Singularity
• Final-State Condition And Dissipative Quantum Mechanics
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox