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BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its...
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BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (30 December 2025) | Viewed by 5358

Special Issue Editors

Prof. Dr. Taoufik Ouali

E-Mail Website
Guest Editor
Laboratory of Physics of Matter and Radiation, Mohammed I University, Oujda BP 717, Morocco
Interests: cosmology; dark energy; dark matter; modified gravity theories; general relativity; early universe
Prof. Dr. Tiberiu Harko

E-Mail Website
Guest Editor
1. Astronomical Observatory, 19 Ciresilor Street, 400487 Cluj-Napoca, Romania
2. Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Interests: modified theories of gravity; cosmology; compact astrophysical objects
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. László Jenkovszky

E-Mail Website
Guest Editor
Bogolyubov Institute for Theoretical Physics (BITP), Ukrainian National Academy of Sciences, 14-b, Metrologicheskaya Str., 03680 Kiev, Ukraine
Interests: high-energy physics
Prof. Ahmed Errahmani

E-Mail Website
Guest Editor
Laboratory of Physics of Matter and Radiation, University of Mohammed First, Oujda BP 717, Morocco
Interests: cosmology; dark energy; dark matter; modified gravity theories; general relativity; early universe; statistical tools
Dr. Amine Bouali

E-Mail Website
Guest Editor
1. Laboratory of Physics of Matter and Radiation, Mohammed I University, Oujda BP 717, Morocco
2. Astrophysical and Cosmological Center, Oujda BP 717, Morocco
3. Higher School of Education and Training, Mohammed I University, Oujda BP 717, Morocco
Interests: cosmology; dark energy; dark matter; modified gravity theories and astrophysics

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to the 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications (BGL2025), https://indico.cern.ch/event/1464707/.

Traditionally, the topics of the Bolyai–Gauss–Lobachevsky conference series cover three main areas:

  • Mathematics: Non-Euclidean and Riemannian geometry;
  • Physics: Non-Euclidian geometries and mathematical methods in modern physics, the cosmology of the early and late Universe, modified gravity theories, quantum mechanics, quantum information, quantum field theory, complex systems, chaos, and nonequilibrium phenomena;
  • History of science: The historical development of Non-Euclidian and Riemannian geometry; the heritage of BGL; significant events in the evolution of science; scientific outreach.

The main goal of the conference, and of this Special Issue, is to create a lively environment in which recent advances in mathematics and physics can be shared between the participants, thus leading to a fruitful interaction and fertile dialogue between practitioners of various branches of mathematics and physics. The conference, as well as the Special Issue, is open to new and innovative ideas that could shape the future landscape of both physics and mathematics.

For this Special Issue, we invite submissions of talks in the following areas: cosmology, modified gravity theories, the Hubble tension, quantum gravity, quantum mechanics, quantum field theory, quantum computation, recent advances in high-energy physics and related fields, gravitational waves, and the physics of complex systems.

There is no maximal length, and the suggested minimum is approx. 4000 words. Submitted papers should contain enough novel contents (except for reviews, which are acceptable from senior contributors). Please note that the three paper types recommended for this special issue are Article, Review, and Communication (limited number). For more details, including various article types, please visit https://www.mdpi.com/about/article_types.

Prof. Dr. Taoufik Ouali
Prof. Dr. Tiberiu Harko
Prof. Dr. László Jenkovszky
Prof. Ahmed Errahmani
Dr. Amine Bouali
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 250 words) can be sent to the Editorial Office for assessment.

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. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. 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

  • advances in mathematics
  • recent developments in physics
  • mathematics–physics dialogue
  • modified gravity theories
  • the Hubble tension
  • quantum gravity
  • cosmology
  • gravitational waves
  • complex systems
  • chaos and instability

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (7 papers)

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Research

Jump to: Review

18 pages, 819 KB  
Article
Jacobi Stability of Circular Orbits Around Conformally Invariant Weyl Gravity Black Holes
by Cristina Blaga and Paul A. Blaga
Universe 2026, 12(4), 114; https://doi.org/10.3390/universe12040114 - 14 Apr 2026
Viewed by 261
Abstract
Weyl conformal gravity was originally proposed in the early twentieth century as an attempt to unify gravitation and electromagnetism. Since 1989, renewed interest in this fourth-order theory of gravity has emerged following the discovery of several exact black hole solutions. In this work, [...] Read more.
Weyl conformal gravity was originally proposed in the early twentieth century as an attempt to unify gravitation and electromagnetism. Since 1989, renewed interest in this fourth-order theory of gravity has emerged following the discovery of several exact black hole solutions. In this work, we investigate the timelike circular geodesics of a spherically symmetric Weyl black hole. The effective potential, the circular geodesics and their Jacobi and Lyapunov stability are discussed. Our analysis provides new insights into the stability properties of Weyl black holes and the role of the free parameters appearing in their solutions. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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12 pages, 384 KB  
Article
Effects of Curvature–Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time
by Volodymyr Gorkavenko, Oleh Barabash, Pavlo Nakaznyi, Mariia Tsarenkova, Nazar Yakovenko and Andrii Zaporozhchenko
Universe 2026, 12(2), 47; https://doi.org/10.3390/universe12020047 - 11 Feb 2026
Viewed by 388
Abstract
We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat (3+1)-dimensional space-time. The defect was modeled as an impenetrable-to-matter-field, finite-thickness tube with magnetic flux inside. We implemented the [...] Read more.
We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat (3+1)-dimensional space-time. The defect was modeled as an impenetrable-to-matter-field, finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We found that in flat space-time, the total vacuum energy generated by a magnetic topological defect depends on the curvature (ξ), except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin’s general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling (ξ), which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary-condition parameter was carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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13 pages, 493 KB  
Article
The Vortex State of Ultralight Dark Matter and the Fornax Timing Problem
by Volodymyr Gorkavenko, Oleh Barabash, Tetiana Gorkavenko, Kateryna Korshynska, Olena Teslyk, Andrii Zaporozhchenko and Eduard Gorbar
Universe 2026, 12(2), 39; https://doi.org/10.3390/universe12020039 - 30 Jan 2026
Viewed by 465
Abstract
We investigate the impact of the vortex state of ultralight dark matter (ULDM) on the dynamical friction acting on moving globular clusters. Comparing this force with that for the solitonic ground state, it is shown that the internal structure and rotation of the [...] Read more.
We investigate the impact of the vortex state of ultralight dark matter (ULDM) on the dynamical friction acting on moving globular clusters. Comparing this force with that for the solitonic ground state, it is shown that the internal structure and rotation of the ULDM core strongly affect the orbital decay of globular clusters. In particular, co-directional rotation in a vortex state can lead to significant suppression of dynamic friction at certain distances where globular clusters and ULDM velocities match. Applying these findings to the Fornax dwarf galaxy, it is found that the Fornax timing problem is naturally alleviated. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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6 pages, 547 KB  
Communication
Strong Progenitor Age Bias in Supernova Cosmology and Alignment with DESI BAO
by Chul Chung, Young-Wook Lee, Junhyuk Son, Seunghyun Park and Hyejeon Cho
Universe 2026, 12(1), 22; https://doi.org/10.3390/universe12010022 - 15 Jan 2026
Viewed by 468
Abstract
Supernova (SN) cosmology is based on the assumption that the luminosity of type Ia SNe, after the luminosity standardization process, remains invariant with progenitor age. However, our comprehensive age measurements of SN host galaxies reveal a significant (5.5σ) correlation between [...] Read more.
Supernova (SN) cosmology is based on the assumption that the luminosity of type Ia SNe, after the luminosity standardization process, remains invariant with progenitor age. However, our comprehensive age measurements of SN host galaxies reveal a significant (5.5σ) correlation between standardized SN luminosity and progenitor age, which is expected to introduce a serious systematic bias with redshift in SN cosmology. After correcting for this age bias with redshift, the SN dataset aligns more closely with the recent DESI BAO result, bringing the updated ’standard candle’ (SNe) into concordance with the ’standard ruler’ (BAO). When the three cosmological probes (SNe, BAO, CMB) are combined, we find a strong (∼9σ) discordance with the ΛCDM model, suggesting a time-varying dark energy equation of state in a currently non-accelerating universe. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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13 pages, 354 KB  
Article
Holographic Thermodynamics of Higher-Dimensional AdS Black Holes with CFT Rescaling
by Yahya Ladghami and Taoufik Ouali
Universe 2025, 11(10), 337; https://doi.org/10.3390/universe11100337 - 10 Oct 2025
Cited by 1 | Viewed by 1269
Abstract
In this paper, we study the thermodynamic behavior of charged AdS black holes in higher-dimensional spacetimes within the framework of conformal holographic extended thermodynamics. This formalism is based on a novel AdS/CFT dictionary in which the conformal rescaling factor of the boundary conformal [...] Read more.
In this paper, we study the thermodynamic behavior of charged AdS black holes in higher-dimensional spacetimes within the framework of conformal holographic extended thermodynamics. This formalism is based on a novel AdS/CFT dictionary in which the conformal rescaling factor of the boundary conformal field theory (CFT) is treated as a thermodynamic parameter, while Newton’s constant is held fixed and the AdS radius is allowed to vary. We explore how variations in the CFT state, represented by its central charge, influence the bulk thermodynamics, phase structure, and stability of black holes in five and six dimensions. Our analysis reveals the emergence of Van der Waals-like phase transitions, critical phenomena governed by the central charge. Additionally, we find that the thermodynamic behavior of AdS black holes is affected by the dimensionality of the bulk spacetime, as we compare higher-dimensional black holes to lower-dimensional ones, such as the BTZ black holes. These findings provide new insights into the role of boundary degrees of freedom in shaping the thermodynamics of gravitational systems via holography. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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13 pages, 283 KB  
Article
Exact Kerr–Schild Spacetimes from Linearized Kinetic Gravity Braiding
by Bence Juhász and László Árpád Gergely
Universe 2025, 11(9), 314; https://doi.org/10.3390/universe11090314 - 12 Sep 2025
Viewed by 1016
Abstract
We generalize our recent work on k-essence sourcing Kerr–Schild spacetimes to the kinetic gravity braiding scalar field. For k-essence, in order for a perturbative Kerr–Schild-type solution to become exact, the k-essence Lagrangian must either be linear in the kinetic term (with the Kerr–Schild [...] Read more.
We generalize our recent work on k-essence sourcing Kerr–Schild spacetimes to the kinetic gravity braiding scalar field. For k-essence, in order for a perturbative Kerr–Schild-type solution to become exact, the k-essence Lagrangian must either be linear in the kinetic term (with the Kerr–Schild congruence autoparallel) or unrestricted, provided the scalar gradient along the congruence vanishes. A similar reasoning for the pure kinetic braiding contribution leads to either a vanishing Lagrangian or a scalar that is constant along the congruence. From the scalar dynamics we also derive an accompanying constraint. Finally, we discuss pp-waves, an example of Kerr–Schild spacetime generated by a constant k-essence along the Kerr–Schild congruence with a vanishing Lagrangian. This allows for the construction of a Fock-type space, consisting of a tower of Kerr–Schild maps first yielding a vacuum pp-wave from flat spacetime; next a k-essence-generated pp-wave from the vacuum pp-wave; and finally an arbitrary number of k-essence pp-waves with different retarded time-dependent metric functions. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

Review

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14 pages, 400 KB  
Review
Towards a Quantum Erlangen Program
by Matthew J. Lake
Universe 2026, 12(3), 84; https://doi.org/10.3390/universe12030084 - 16 Mar 2026
Viewed by 323
Abstract
The classical Erlangen Program sought to classify metric spaces entirely in terms of their symmetries. In physical spacetimes, these symmetries define transformations between classical reference frames, yielding a one-to-one correspondence between frame transformations and the underlying geometry. More recently, the classical notion of [...] Read more.
The classical Erlangen Program sought to classify metric spaces entirely in terms of their symmetries. In physical spacetimes, these symmetries define transformations between classical reference frames, yielding a one-to-one correspondence between frame transformations and the underlying geometry. More recently, the classical notion of an ideal frame has been extended to the quantum regime, by considering observers as embodied physical systems, subject to the laws of quantum mechanics. Here, we build on this approach, but outline an alternative definition of the term ‘quantum reference frame’, which differs somewhat from the mainstream view. We then show how the new definition can be used to construct a simple model of Planck-scale spacetime, which makes contact with existing quantum gravity phenomenology. Finally, we show how classical spacetime symmetries can be ‘mathematically preserved but operationally broken’ using the new model, suggesting that quantum spacetime may be classified, at least locally, in terms of transformations between quantised frames of reference. This work is based on a talk given at the 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry in Oujda, Morocco, in May 2025. Full article
(This article belongs to the Special Issue BGL2025: The 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)
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