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Entropy
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Quantum Regularization of Singular Black Hole Solutions
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Quantum Regularization of Singular Black Hole Solutions

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: closed (10 June 2022) | Viewed by 6943

Special Issue Editor

Prof. Dr. Massimo Tessarotto

E-Mail Website
Guest Editor
Department of Mathematics and Geosciences, University of Trieste, 34100 Trieste, Italy
Interests: quantum mechanics; general relativity; quantum field theory; special and general relativity; turbulence modeling; theoretical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is generally acknowledged that space–time singularities, particularly black hole (BH) ones, play an essential role in general relativity (GR), due to their widespread nature. On the other hand, the very existence of such singularities represents a crucial conceptual issue, possibly related to the limits of the validity of GR itself, since these singularities cannot be resolved/cured in the framework of classical GR or by reverting to higher-order curvature and non-local models of classical gravity. On the contrary, the prevailing opinion is that such singularities should be regarded as strong signatures of possible quantum effects, potentially occurring in the presence of intense gravitational fields. This explains why, nowadays, one of the most promising areas of theoretical astrophysics lies probably in the investigation of strong field regimes of gravity in and around BHs. In such a context, in fact, theoretical models can be tested through the direct observation and detection of gravitational waves, radiation emissions from ultra-relativistic charged particles and evaluation or measurement of the remote gravitational fields.

Consequently, an unanswered question concerns what the expected characteristic features of such gravitational fields should be. Thus, a proper understanding of the role of quantum gravity is urgently needed and would be profoundly meaningful. Nevertheless, the identification of the relevant quantum phenomenology depends very much on the precise choice of the model of quantum gravity to be adopted. The goal of this Special Issue is to offer a privileged stage for a specialized debate on the subject, with the purpose of advancing tentative answers to such a fundamental question. To this end, review articles, as well as original research works, will be presented. Emphasis will be placed in particular on a number of difficult/unsolved related issues, including:

  • How quantum gravity models can cure BH singularities, giving rise to a suitable quantum-modified background metric field tensor (MFT);
  • The possible signatures and experimental evidence which may characterize the same MFT;
  • The possible large-scale effects produced by local quantum modifications of MFT;
  • The possible role of the cosmological constant and how its quantum character could be significant for the regularization of singular space–time solutions.

Prof. Dr. Massimo Tessarotto
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Manifest covariance
  • Hamiltonian theory of GR
  • Covariant quantum gravity
  • Quantum-modified Einstein field equation
  • Cosmological constant

Published Papers (3 papers)

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Research

20 pages, 342 KiB  
Article
Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity
by Claudio Cremaschini and Massimo Tessarotto
Entropy 2021, 23(5), 511; https://doi.org/10.3390/e23050511 - 23 Apr 2021
Cited by 3 | Viewed by 1818
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 [...] Read more.
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 δr 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 δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. 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. Full article
(This article belongs to the Special Issue Quantum Regularization of Singular Black Hole Solutions)
27 pages, 409 KiB  
Article
The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity
by Massimo Tessarotto and Claudio Cremaschini
Entropy 2021, 23(3), 370; https://doi.org/10.3390/e23030370 - 20 Mar 2021
Cited by 3 | Viewed by 1696
Abstract
An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum [...] Read more.
An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics. Full article
(This article belongs to the Special Issue Quantum Regularization of Singular Black Hole Solutions)
33 pages, 432 KiB  
Article
The Principle of Covariance and the Hamiltonian Formulation of General Relativity
by Massimo Tessarotto and Claudio Cremaschini
Entropy 2021, 23(2), 215; https://doi.org/10.3390/e23020215 - 10 Feb 2021
Cited by 12 | Viewed by 2735
Abstract
The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the [...] Read more.
The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out. Full article
(This article belongs to the Special Issue Quantum Regularization of Singular Black Hole Solutions)
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