Energy-momentum tensor and metric near the Schwarzschild sphere

Abstract

Regularity of the horizon radius $r_g$ of a collapsing body constrains a limiting form of a spherically-symmetric energy-momentum tensor near it. Its non-zero limit belongs to one of four classes that are distinguished only by two signs. As a result, close to $r_g$ the geometry can always be described by either an ingoing or outgoing Vaidya metric with increasing or decreasing mass. If according to a distant outside observer the trapped regions form in finite time, then the Einstein equations imply violation of the null energy condition. In this case the horizon radius and its rate of change determine the metric in its vicinity, and the hypersurface $r=r_g(t)$ is timelike during both the expansion and contraction of the trapped region. We present the implications of these results for the firewall paradox and discuss arguments that the required violation of the null energy condition is incompatible with the standard analysis of black hole evaporation.

arXiv comment10 pages. Published version

References in corpus (24)

• Formation and evaporation of non-singular black holes
• Sinc approximation of algebraically decaying functions
• The Physics of Maxwell's demon and information
• The observational evidence for horizons: from echoes to precision gravitational-wave physics
• Tests for the existence of horizons through gravitational wave echoes
• A Primer for Black Hole Quantum Physics
• Black hole evaporation: A paradigm
• Black Hole Remnants and the Information Loss Paradox
• The physics of forgetting: Landauer's erasure principle and information theory
• Warp drive basics
• McVittie's Legacy: Black Holes in an Expanding Universe
• Hawking-like radiation from evolving black holes and compact horizonless objects
• Physical observability of horizons
• Versatile method for renormalized stress-energy computation in black-hole spacetimes
• Singularity theorems from weakened energy conditions
• How the expansion of the universe determines the causal structure of McVittie spacetimes
• Radiation from collapsing shells, semiclassical backreaction and black hole formation
• Quantum Energy Inequalities and local covariance I: Globally hyperbolic spacetimes
• Role of evaporation in gravitational collapse
• Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime
• Closed trapping horizons without singularity
• A singularity theorem for Einstein-Klein-Gordon theory
• The information recovery problem
• Smooth and sharp creation of a spherical shell for a $(3+1)$-dimensional quantum field

Cited by in corpus (24)

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• Pandora's box lid: geometry near the apparent horizon
• Universal properties of the near-horizon geometry
• Kerr-Vaidya black holes
• Paradoxes before the paradox: surface gravity and the information loss problem
• Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes
• Semiclassical black holes and horizon singularities
• Matter and forces near physical black holes
• Physical black holes in fourth-order gravity
• Kinematic and energy properties of dynamical regular black holes
• Unruh-DeWitt Detector Differentiation of Black Holes and Exotic Compact Objects
• Spherically symmetric black holes in metric gravity
• On Firewalls in quantum-corrected General Relativity
• Inaccessibility of traversable wormholes
• Physical black holes in semiclassical gravity
• Distance between collapsing matter and trapping horizon in evaporating black holes
• Horizon-bound objects: Kerr--Vaidya solutions
• Exotic Encounters: Buchdahl's Conditions and Physical Black Holes
• Semi-classical imprints on quasinormal mode spectra
• Black holes and their horizons in semiclassical and modified theories of gravity
• Constraining modified gravity theories with physical black holes