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Axioms
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Theory and Mathematical Aspects of Black Holes
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Theory and Mathematical Aspects of Black Holes

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 10003

Special Issue Editors

Prof. Dr. Irina Radinschi

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Guest Editor
Department of Physics, “Gheorghe Asachi” Technical University, 700050 Iasi, Romania
Interests: general relativity and cosmology; computational physics; string theory
Special Issues, Collections and Topics in MDPI journals
Dr. Theophanes Grammenos

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Guest Editor
Department of Civil Engineering, University of Thessaly, 383 34 Volos, Greece
Interests: mathematical physics; general relativity; differential geometry; differential equations
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Prof. Dr. Farook Rahaman

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Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India
Interests: mathematical physics; relativity; cosmology and astrophysics
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Prof. Dr. Saibal Ray

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Centre for Cosmology, Astrophysics and Space Science (CCASS) GLA University, 17th KM Mile Stone, NH-2, Mathura-Delhi Highway Road, P.O. Chaumuhan, Mathura 281406, Uttar Pradesh, India
Interests: general relativity; stellar astrophysics; brane-world model and galactic dynamics; dark energy theory; cosmic expansion
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Dr. Marius-Mihai Cazacu

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Guest Editor
Department of Physics, “Gh. Asachi” Technical University, Iasi 700050, Romania
Interests: physics; optics and spectroscopy; environmental; aerosols
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Special Issue Information

Dear Colleagues,

More than 80 years have passed since S. Chandrasekhar showed that a sufficiently massive body cannot remain in hydrostatic equilibrium and must inevitably undergo a complete gravitational collapse, leading to the formation of a black hole. Today, despite a plethora of observational data supporting the existence of astrophysical black holes, culminated with the gravitational waves that are emitted during the merging of two black holes and detected by LIGO, and a considerable amount of theoretical work regarding their properties, behavior, and evolution on the basis of the predictions of General Relativity and initiated by the monumental paper of R. Oppenheimer and H. Snyder in 1939, there are still many questions that remain unsolved and keep the theoretical and mathematical study of black holes a vivid, fascinating, and ongoing subject of theoretical and mathematical physics. Such issues refer to, but are certainly not limited to, the problem of energy–momentum localization, the possible existence and description of black holes in higher dimensions, the geometry and topology of the event horizon, the thermodynamics of black holes, quantum black holes in the context of the behavior of General Relativity in the quantum regime, and the mathematical and conceptual analysis of black holes and their singularities from the point of view of partial differential equations.

This Special Issue will focus on theoretical and mathematical problems of black holes, of classical as well as quantum character. In this sense, original research or review articles in the following areas are welcome:

  • Black hole formation
  • Black hole stability
  • Wave equations in black hole space-times
  • Energy–momentum localization
  • Quantum black holes
  • Black hole thermodynamics
  • Black hole accretion discs
  • Black hole gravitational radiation
  • Higher-dimensional black holes
  • Topological black holes
  • Stringy black holes
  • Acoustic black holes
  • Naked singularity of black holes
  • Future possibilities of black holes

Prof. Dr. Irina Radinschi
Assoc. Prof. Theophanes Grammenos
Prof. Dr. Farook Rahaman
Assoc. Prof. Saibal Ray
Dr. Marius-Mihai Cazacu
Guest Editors

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. Axioms 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 2400 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.

Published Papers (4 papers)

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Research

24 pages, 479 KiB  
Article
Revisiting Primordial Black Hole Evolution
by Maxim Khlopov, Biplab Paik and Saibal Ray
Axioms 2020, 9(2), 71; https://doi.org/10.3390/axioms9020071 - 25 Jun 2020
Cited by 3 | Viewed by 2432
Abstract
Primordial black holes (PBHs) are the sensitive probe for physics and cosmology of very early Universe. The observable effect of their existence depends on the PBH mass. Mini PBHs evaporate and do not survive to the present time, leaving only background effect of [...] Read more.
Primordial black holes (PBHs) are the sensitive probe for physics and cosmology of very early Universe. The observable effect of their existence depends on the PBH mass. Mini PBHs evaporate and do not survive to the present time, leaving only background effect of products of their evaporation, while PBHs evaporating now can be new exotic sources of energetic particles and gamma rays in the modern Universe. Here we revisit the history of evolution of mini PBHs. We follow the aspects associated with growth versus evaporation rate of “a mini PBH being trapped inside intense local cosmological matter inhomogeneity”. We show that the existence of baryon accretion forbidden black hole regime enables constraints on mini PBHs with the mass M ≤ 5.5 × 10 13 g. On the other hand, we propose the mechanism of delay of evaporation of primordial population of PBHs of primordial mass range 5.5 × 10 13 g ≤ M ≤ 5.1 × 10 14 g. It can provide their evaporation to be the main contributor to γ -ray flux distribution in the current Universe. At the final stage of evaporation these PBHs can be the source of ultrahigh energy cosmic rays and gamma radiation challenging probe for their existence in the LHAASO experiment. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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8 pages, 329 KiB  
Article
Vaidya Collapse with Nonzero Radial Pressure and Charge
by Aroonkumar Beesham
Axioms 2020, 9(2), 52; https://doi.org/10.3390/axioms9020052 - 13 May 2020
Cited by 1 | Viewed by 2016
Abstract
The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We [...] Read more.
The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We discuss the collapse of a fluid with nonzero radial pressure within the context of the Vaidya spacetime considering a decaying cosmological parameter as well as nonzero charge. Previously, a similar analysis was done, but without considering charge. A decaying cosmological parameter may also be associated with dark energy. We found that both black holes and naked singularities can form, depending upon the initial conditions. Hence, charge does not restore the validity of the hypothesis. This provides another example of the violation of the cosmic censorship hypothesis. We also discuss some radiating rotating solutions, arriving at the same conclusion. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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14 pages, 463 KiB  
Article
Quasinormal Modes of Charged Black Holes in Higher-Dimensional Einstein-Power-Maxwell Theory
by Grigoris Panotopoulos
Axioms 2020, 9(1), 33; https://doi.org/10.3390/axioms9010033 - 24 Mar 2020
Cited by 14 | Viewed by 3266
Abstract
We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the [...] Read more.
We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the test scalar field is investigated in detail. The quasinormal spectra in the eikonal limit are computed as well for several different space-time dimensionalities. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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13 pages, 303 KiB  
Article
Systolic Aspects of Black Hole Entropy
by Nikolaos Kalogeropoulos
Axioms 2020, 9(1), 30; https://doi.org/10.3390/axioms9010030 - 16 Mar 2020
Viewed by 1653
Abstract
We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections Σ of the horizon. This is not forbidden by topological censorship, since [...] Read more.
We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections Σ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of Σ are violated in quantum theory. We choose the systoles of Σ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of Σ . We focus on the limiting case of Σ having a large genus. Full article
(This article belongs to the Special Issue Theory and Mathematical Aspects of Black Holes)
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