The quantum fate of black hole horizons

Abstract

The presence of a horizon is the principal marker for black holes as they appear in the classical theory of gravity. In General Relativity (GR), horizons have several defining properties. First, there exists a static spherically symmetric solution to vacuum Einstein equations which possesses a horizon defined as a null-surface on which the time-like Killing vector becomes null. Second, in GR, a co-dimension two sphere of minimal area is necessarily a horizon. On a quantum level, the classical gravitational action is supplemented by the quantum effective action obtained by integrating out the quantum fields propagating on a classical background. In this note we consider the case when the quantum fields are conformal and perform a certain non-perturbative analysis of the semiclassical equations obtained by varying the complete gravitational action. We show that, for these equations, both of the above aspects do not hold. More precisely, we prove that i) a static spherically symmetric metric that would describe a horizon with a finite Hawking temperature is, generically, {\it not} a solution; ii) a minimal $2$-sphere is {\it not} a horizon but a tiny throat of a wormhole. We find certain bounds on the norm of the Killing vector at the throat and show that it is, while non-zero, an exponentially small function of the Bekenstein-Hawking (BH) entropy of the classical black hole. We also find that the possible temperature of the semiclassical geometry is exponentially small for large black holes. These findings suggest that a black hole in the classical theory can be viewed as a certain (singular) limit of the semiclassical wormhole geometry. We discuss the possible implications of our results.

arXiv comment17 pages, no figures; title slightly changed, more remarks, new footnotes and references, version to appear in PLB

References in corpus (33)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Eternal Black Holes in AdS
• Is the gravitational-wave ringdown a probe of the event horizon?
• Can environmental effects spoil precision gravitational-wave astrophysics?
• Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale
• BlackCAT: A catalogue of stellar-mass black holes in X-ray transients
• The observational evidence for horizons: from echoes to precision gravitational-wave physics
• Tests for the existence of horizons through gravitational wave echoes
• Wormholes as Black Hole Foils
• Weyl Cohomology and the Effective Action for Conformal Anomalies
• Echoes of Kerr-like wormholes
• Classical black hole evaporation in Randall-Sundrum infinite braneworld
• Information loss problem and a `black hole' model with a closed apparent horizon
• On Quantum Deformation of the Schwarzschild Solution
• Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
• Wormholes versus black holes: quasinormal ringing at early and late times
• Semiclassical Extremal Blackholes
• Wavefunction of a Black Hole and the Dynamical Origin of Entropy
• On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes
• Information Consumption by Reissner-Nordstrom Black Holes
• Finite temperature nonlocal effective action for quantum fields in curved space
• Poincare Recurrences and Topological Diversity
• Restoring Unitarity in BTZ Black Hole
• Horizon Holography
• Adiabatic Regularization for Gauge Field and the Conformal Anomaly
• Static Black Holes With Back Reaction From Vacuum Energy
• The detection of Quasinormal Mode of Pop III Binary Black Hole merger with final $M\sim 60M_{\odot }$ and $a/M\sim 0.7$ would confirm the strong gravity space-time around $\sim 2M$ which is only $\sim 1.17$ times the event horizon radius
• Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid
• Universal Features of Four-Dimensional Superconformal Field Theory on Conic Space
• Comparison theorems for causal diamonds
• Planckian $Ad{S}_2\times S_2$ space is an exact solution of the semiclassical Einstein equations
• One-loop conformal anomaly in an implicit momentum space regularization framework
• Firewalls as artefacts of inconsistent truncations of quantum geometries

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• From micro to macro and back: probing near-horizon quantum structures with gravitational waves
• Towards VLBI Observations of Black Hole Structure
• Semiclassical constant-density spheres in a regularized Polyakov approximation
• Schwarzschild geometry counterpart in semiclassical gravity
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• Wormholes in conformal gravity
• Anatomy of a thermal black hole mimicker
• Logarithmic terms in entropy of Schwarzschild black holes in higher loops
• Reissner-Nordström geometry counterpart in semiclassical gravity
• On the Near-Horizon Geometry of an Evaporating Black Hole
• An Analytic Description of Semi-Classical Black-Hole Geometry
• Back Reaction of 4D Conformal Fields on Static Geometry
• On the Inverse Spectrum Problem of Neutron Stars
• Particle creation in gravitational collapse to a horizonless compact object
• Asymptotically flat vacuum solutions in order-reduced semiclassical gravity
• Quantum states and their back-reacted geometries in 2d dilaton gravity
• Burst particle creation in gravitational collapse to a horizonless compact object
• Space-time structure, asymptotic radiation and information recovery for a quantum hybrid state
• Hybrid quantum states in 2d dilaton gravity
• Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity
• Damour-Solodukhin Wormhole as a Black Hole Mimicker: The Role of Observers' Location
• Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity
• On a Class of Harko-Kovacs-Lobo Wormholes
• Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds
• Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass