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Axioms
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Mathematical Aspects of Black Holes in General Relativity and Beyond
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Mathematical Aspects of Black Holes in General Relativity and Beyond

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Hilbert’s Sixth Problem".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 2199

Special Issue Editor

Dr. Mehrab Momennia

E-Mail Website
Guest Editor
Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico
Interests: general relativity; gravitation; black hole physics; relativistic astrophysics; black hole perturbation theory; black hole thermodynamics; modified gravity; quasinormal modes of black holes; cosmology

Special Issue Information

Dear Colleagues,

A valid gravitational theory for explaining black hole physics and cosmology should be compatible with the existing observational data from black holes and cosmos. Although Einstein’s gravity, which was built on a rigorous geometric structure, describes the current epoch of the universe quite well, it suffers some defects in describing the galaxy rotation curves, accelerated expansion of the universe, and Hubble tension, among others. On the other hand, the curvature singularity located at the center of the black holes remains a crucial and outstanding problem in Einstein’s theory of relativity.

In order to overcome the aforementioned shortcomings to describe black hole physics and the cosmos in a complete way, one can attempt to develop gravitational theories beyond general relativity or consider various matter fields through advanced tensor analysis and spacetime symmetries.

This Special Issue is dedicated to the deep mathematical aspects of black holes and cosmology in Einstein’s gravity, coupled with various matter sources and modified theories of gravitation involving nonlinear differential equations and topological invariants. This Special Issue covers the original contributions in modified gravity, black hole and wormhole solutions with singular hypersurfaces, black hole perturbation theory, quasinormal modes linked to spectral theory, advanced mathematics in relativistic astrophysics, accretion disks, relativistic kinetic theory, nonlinear electrodynamics embedded in gauge field frameworks, black hole thermodynamics, geometrical thermodynamics with manifold embeddings, quantum corrected black holes, AdS/CFT correspondence bridging conformal field theories, and gravitational waves analyzed through harmonic oscillators, but is not limited to these research fields.

Dr. Mehrab Momennia
Guest Editor

Manuscript Submission Information

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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.

Keywords

  • gravitational waves
  • modified gravity models
  • AdS/CFT correspondence
  • nonlinear electrodynamics
  • black hole thermodynamics
  • geometrical thermodynamics
  • quantum-corrected black holes
  • black hole and wormhole solutions
  • relativistic astrophysics and accretion disks
  • relativistic kinetic theory on curved spacetime
  • black hole perturbation theory and quasinormal modes
  • metric tensor
  • geodesic equations
  • Einstein’s field equations and beyond

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Published Papers (2 papers)

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17 pages, 459 KB  
Article
The Conservative Field of Coupled Newton–Coulomb Sources: Component Coupling Constants, Mass ⇌ Charge Cross-Forces, and Radiation from Reissner–Nordström Black Hole Mergers
by Dimitris M. Christodoulou, Demosthenes Kazanas and Silas G. T. Laycock
Axioms 2025, 14(11), 845; https://doi.org/10.3390/axioms14110845 - 18 Nov 2025
Viewed by 571
Abstract
We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine [...] Read more.
We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine the coupling constant of the cross-field components as the geometric mean (G-M) of Newton’s G and Coulomb’s K constants, in both SI units and dimensionless form. Consequently, for two identical objects, the cross-force (F×) is the G-M of the familiar Newton (Fg) and Coulomb (Fe) forces, so that F×=FgFe, where Fg≪F×≪Fe. Remarkably, such cross-forces should be measurable in torsion balance experiments involving a suspended neutral mass interacting with a partially ionized gas. Furthermore, we apply our new formulation to estimate the dimensionless amplitude ∥hαβTT∥ of gravitational waves that are emitted by inspiraling Reissner–Nordström (RN) black hole binaries, expressed in terms of ratios of the four fundamental lengths of the problem: the distance to the binary D, the binary separation R, the Schwarzschild radius RS∝2M of mass M, and the RN charge (Q) length scale LQ∝2Q. In this classical setting with speeds much lower than the speed of light c in vacuum, the surprising appearance of the maximum relativistic tension force Fmax=c4/(4G) is duly noted. Full article
(This article belongs to the Special Issue Mathematical Aspects of Black Holes in General Relativity and Beyond)
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20 pages, 36430 KB  
Article
A Brief Review of Wormhole Cosmic Censorship
by Leonel Bixano, I. A. Sarmiento-Alvarado and Tonatiuh Matos
Axioms 2025, 14(11), 831; https://doi.org/10.3390/axioms14110831 - 11 Nov 2025
Viewed by 1216
Abstract
Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here [...] Read more.
Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole “sucks in” the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein–Maxwell–Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship. Full article
(This article belongs to the Special Issue Mathematical Aspects of Black Holes in General Relativity and Beyond)
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