Abstract
A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as ; (b) for supermassive black holes is typically orders of magnitude larger than the Planck length . Instead, for typical stellar-mass black holes, may drop well below . The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.
Highlights
This paper is part of the research effort devoted to the quantum regularization of singular classical black hole (BH) solutions
The expression of the Hawking temperature defined on such a surface was carried out. This proved that the stochastic behavior of quantum gravity can affect the thermodynamic description of continuum gravitational field and the related particle-tunnelling effect that might arise across the stochastic horizon boundary in a non-trivial way
The theory of General Relativity is characterized by the occurrence of classical singularitites in the space–time metric tensor solution of the Einstein field equations
Summary
This paper is part of the research effort devoted to the quantum regularization of singular classical black hole (BH) solutions. This proved that the stochastic behavior of quantum gravity can affect the thermodynamic description of continuum gravitational field and the related particle-tunnelling effect that might arise across the stochastic horizon boundary in a non-trivial way These premises suggest, at least, the obvious possibility that the radius of black hole event horizons should not be regarded as a deterministic quantity. In such a case, a particle might have a finite probability density of simultanrously being either “in” or “out” with respect to a stochastic surface which is no-longer prescribed as a deterministic barrier Given these premises, this paper is intended to be a continuation of previous research effort dealing with the investigation of the quantum modifications/corrections to the structure of classical black holes and the physics of event horizons in the presence of stochastic gravitational fields. The resulting tunneling effect yields a background-dependent model which is affected by the black hole mass, which, in turn, generates the curved space–time itself
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