The state of Hawking radiation is non-classical

Abstract

We show that the state of the Hawking radiation emitted from a large Schwarzschild black hole (BH) deviates significantly from a classical state, in spite of its apparent thermal nature. For this state, the occupation numbers of single modes of massless asymptotic fields, such as photons, gravitons and possibly neutrinos, are small and, as a result, their relative fluctuations are large. The occupation numbers of massive fields are much smaller and suppressed beyond even the expected Boltzmann suppression. It follows that this type of thermal state cannot be viewed as classical or even semiclassical. We substantiate this claim by showing that, in a state with low occupation numbers, physical observables have large quantum fluctuations and, as such, cannot be faithfully described by a mean-field or by a WKB-like semiclassical state. Since the evolution of the BH is unitary, our results imply that the state of the BH interior must also be non-classical when described in terms of the asymptotic fields. We show that such a non-classical interior cannot be described in terms of a semiclassical geometry, even though the average curvature is sub-Planckian.

Non‐Singular Black Holes Interiors Need Physics Beyond the Standard Model

“…There, it is shown that the BH radiation is in a highly quantum state when expressed in terms of the Fock (or occupation number) basis of asymptotic quantum fields. It follows that the purifier of the radiation — the BH interior — is of a similarly quantum nature when expressed in the corresponding basis (this is also shown explicitly in []). Our conclusion is that a geometrical description of the interior in terms of a semiclassical metric is not feasible.…”

“…The polymer model grew out of the notion that the BH interior must be in a non‐classical state, even at times before the Page time. This claim has been a common theme in some of our recent work, beginning with [], but the most explicit argument is presented in []. There, it is shown that the BH radiation is in a highly quantum state when expressed in terms of the Fock (or occupation number) basis of asymptotic quantum fields.…”

Resisting collapse: How matter inside a black hole can withstand gravity

“…The model is described in detail in [30] and we will review its main ingredients here for completeness. This proposal was inspired in part by [33,34] and motivated by the observation that the BH interior has to be in a strongly non-classical state [29,35,36], even at times well before the Page time [37]. Fundamental strings could be produced out of whatever form of matter that collapses into a BH-like object, as long as the resulting string state is entropically favored.…”

“…This "internal" equation of state reveals that signals propagate at the speed of light along a closed string. It is not, however, a statement about the interior geometry, as a semiclassical description of the metric is invalidated by strong quantum fluctuations [29,36].…”

Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon

“…In this reference, additional challenging questions include the role that event horizons undertake in classical and quantum descriptions of general relativity, the nature of their existence as space-time frontiers and their mathematical description, and the inspection of quantum physical and thermodynamics phenomena that can occur in their surroundings as a consequence of interaction with particles and fields, including the gravitational field itself [ 19 , 20 , 21 , 22 , 23 ]. In fact, event horizons may be characterized by the occurrence of energetic particle phenomena and collective interactions, and for this reason, they are also expected to provide the background for quantum field phenomena, which may ultimately involve also the dynamics of the same gravitational field [ 24 , 25 , 26 ], the physics of event horizons [ 27 ], as exemplified by particle emission and acceleration mechanisms [ 28 ], and phenomena related to entropy creation/conservation [ 29 , 30 , 31 , 32 ].…”