Recent Advance in Mathematical Physics II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 3400

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Dipartimento di Meccanica, Matematica and Management, Politecnico di Bari, 70125 Bari, Italy
Interests: variational and topological methods in nonlinear analysis; geometric analysis; geometric variational problems
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Special Issue Information

Dear Colleagues, 

This Special Issue of Symmetry is devoted to the most recent and valuable developments in mathematical physics that are of theoretical or applicable interest. More attention will be paid to problems and models which present a symmetric feature. 

We expect contributions from all fields covered by mathematical physics, in particular from the following fields: 

  • Geometric methods in mathematical physics, including dynamical systems, geometric mechanics, special and general relativity, Einstein equations, and quantum gravity;
  • Linear and nonlinear partial differential equations of mathematical physics, such as linear and nonlinear Schrodinger equations, Maxwell equations, Klein–Gordon equations, and systems of partial differential equations;
  • Continuum mechanics and applications to mechanical engineering;
  • Fluid mechanics and applications. 

We look forward to your contributions to this Special Issue. 

Prof. Dr. Antonio Masiello
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. Symmetry 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.

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Published Papers (3 papers)

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Research

21 pages, 2025 KiB  
Article
Global Models of Collapsing Scalar Field: Endstate
by Dario Corona and Roberto Giambò
Symmetry 2024, 16(5), 583; https://doi.org/10.3390/sym16050583 - 9 May 2024
Viewed by 783
Abstract
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data [...] Read more.
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed by Einstein’s equations, considering variations in parameters that influence naked singularity formation. We illustrate how these results apply to a family of scalar field models, concluding with a discussion on the concept of genericity in singularity studies. Full article
(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
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11 pages, 279 KiB  
Article
Pseudo-Finsler Radially Symmetric Spaces
by Marianty Ionel and Miguel Ángel Javaloyes
Symmetry 2024, 16(3), 362; https://doi.org/10.3390/sym16030362 - 18 Mar 2024
Viewed by 974
Abstract
We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversibility. As a consequence, reversible pseudo-Finsler manifolds with [...] Read more.
We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversibility. As a consequence, reversible pseudo-Finsler manifolds with constant flag curvature are radially symmetric. Full article
(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
64 pages, 726 KiB  
Article
A Unified Perspective on Poincaré and Galilei Relativity: I. Special Relativity
by Christian Y. Cardall
Symmetry 2024, 16(2), 214; https://doi.org/10.3390/sym16020214 - 10 Feb 2024
Viewed by 939
Abstract
A semantic adjustment to what physicists mean by the terms ‘special relativity’ and ‘general relativity’ is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincaré group and physics governed by the Galilei group. After exploring [...] Read more.
A semantic adjustment to what physicists mean by the terms ‘special relativity’ and ‘general relativity’ is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincaré group and physics governed by the Galilei group. After exploring the limits of a unified perspective available in the setting of 4-dimensional spacetime, a particular central extension of the Poincaré group—analogous to the Bargmann group that is a central extension of the Galilei group—is presented that deepens a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting. The immediate focus of this paper is classical physics on affine 4-dimensional and 5-dimensional spacetimes (‘special relativity’ as redefined here), including the electrodynamics that gave rise to Poincaré physics in the first place, but the results here may suggest the existence of a ‘Galilei general relativity’ more extensive than generally known, to be pursued in the sequel. Full article
(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
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