Evaporation of four-dimensional dynamical black holes sourced by the quantum trace anomaly

Abstract

We study the evaporation of a four-dimensional spherically symmetric black hole formed in a gravitational collapse. We analyze the back-reaction of a massless quantum scalar field conformally coupled to the scalar curvature by means of the semiclassical Einstein equations. We show that the evaporation is linked to an ingoing negative energy flux at the dynamical horizon and that this flux is induced by the quantum matter trace anomaly outside the black hole horizon whenever a suitable averaged energy condition is satisfied. For illustrative purposes, we evaluate the negative ingoing flux and the corresponding rate of evaporation in the case of a null radiating star described by the Vaidya spacetime.

arXiv comment21 pages, 2 figure. Changed abstract and introduction, modified section 3, added figure about the smearing function. Added some references and made minor corrections. Made slightly modifications of the ANEC and of the smearing function presented in the statement of Theorem 4.1 (p.10). Added corrections to the final part of the proof of Theorem 4.1

References in corpus (43)

• Hawking Radiation as Tunneling
• Isolated and dynamical horizons and their applications
• The Thermodynamics of Black Holes
• General Laws of Black-Hole Dynamics
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Gravitational Energy in Spherical Symmetry
• The generally covariant locality principle -- A new paradigm for local quantum physics
• Dynamical Horizons and their Properties
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Averaged Energy Conditions and Quantum Inequalities
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Dynamic black-hole entropy
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Tunnelling Methods and Hawking's radiation: achievements and prospects
• Semiclassical Gravity Theory and Quantum Fluctuations
• Quantum fields in curved spacetime
• Energy conditions in general relativity and quantum field theory
• Restrictions on Negative Energy Density in Flat Spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Quantum inequalities in two dimensional Minkowski spacetime
• On the Hawking radiation as tunneling for a class of dynamical black holes
• Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• Null energy conditions in quantum field theory
• Surprises in the Evaporation of 2-Dimensional Black Holes
• Evaporation of 2-Dimensional Black Holes
• Probability distributions of smeared quantum stress tensors
• Averaged Energy Conditions and Evaporating Black Holes
• Black hole evaporation without an event horizon
• Stability of quantum systems at three scales: Passivity, quantum weak energy inequalities and the microlocal spectrum condition
• Local Thermal Equilibrium States and Quantum Energy Inequalities
• Temperature and entropy-area relation of quantum matter near spherically symmetric outer trapping horizons
• Holography and trace anomaly: what is the fate of (brane-world) black holes?
• A singularity theorem for Einstein-Klein-Gordon theory
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Boundary Terms and Noether Current of Sphereical Black Holes
• A new derivation of singularity theorems with weakened energy hypotheses
• Probability Distributions for Space and Time Averaged Quantum Stress Tensors
• Method to compute the stress-energy tensor for a quantized scalar field when a black hole forms from the collapse of a null shell
• Space and Time Averaged Quantum Stress Tensor Fluctuations
• Black holes: new horizons
• Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models

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• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
• Global Hyperbolicity and Self-adjointness