Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

• Main Authors: Claudio Cremaschini, Massimo Tessarotto
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Entropy
• Subjects: covariant quantum gravity; cosmological constant; Schwarzschild–deSitter space-time; event horizon; stochastic effects; tunneling phenomena
• Online Access: https://www.mdpi.com/1099-4300/23/5/511

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mi>r</mi></mrow></semantics></math></inline-formula> between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass <i>M</i> of the black hole, scaling as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mi>r</mi><mo>∼</mo><msup><mi>M</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula>; (b) for supermassive black holes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mi>r</mi></mrow></semantics></math></inline-formula> is typically orders of magnitude larger than the Planck length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mi>P</mi></msub></semantics></math></inline-formula>. Instead, for typical stellar-mass black holes, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mi>r</mi></mrow></semantics></math></inline-formula> may drop well below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mi>P</mi></msub></semantics></math></inline-formula>. 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.