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.

21 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

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Cited by in corpus (6)

• Universal definition of the non-conformal trace anomaly
• On the initial value problem for semiclassical gravity without and with quantum state collapses
• Linear stability of semiclassical theories of gravity
• Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect
• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
• Global Hyperbolicity and Self-adjointness