Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.6
Journals
Axioms
Special Issues
Mathematical Physics in General Relativity Theory
share announcement

Mathematical Physics in General Relativity Theory

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 886

Special Issue Editor

Dr. Orchidea Maria Lecian

E-Mail Website
Guest Editor
1. Department of Medicine and Pharmacy & Department of Medicine and Dentistry, Sapienza University of Rome, 00185 Rome, Italy
2. ICRA-International Center for Relativistic Astrophysics C/O Physics Department, Sapienza University of Rome, Piazzale Aldo Moro, 5-00185 Rome, Italy
3. ICRANet- International Center for Relativistic Astrophysics Network, Piazza della Repubblica, 65122 Pescara, Italy
Interests: physics; mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue mainly focuses on the complex relations between mathematical principles and general relativity (GR) in mathematical physics.

  • The following aspects are included:
  • The initial conditions of the Einstein field equations are studied;
  • The initial conditions of the components of the metric tensor are analyzed;
  • Special interest in the study of Cauchy surfaces;
  • The hyperbolic character of the field equations is outlined;
  • Quantum-gravitational theories are also considered: for example,
  • Quantum aspects of the cosmological singularity are reared to concerning what aspects of the theorems of quantum gravity allow for a proper definition of the Cauchy surfaces.

By studying the above themes, we would like to develop further discussion on the mathematical foundation of general relativity and its initial value problem and a deeper understanding of the implications of quantum gravity in defining the structure of space–time.

Dr. Orchidea Maria Lecian
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 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. 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

  • general relativity
  • mathematical physics
  • differential geometry
  • curvature and topology
  • cosmological models
  • quantum gravity
  • numerical relativity
  • einstein's equations
  • spacetime manifolds
  • metric tensor
  • initial conditions
  • cauchy surfaces
  • hyperbolic equations
  • quantum gravity
  • cosmological singularities
  • well posedness
  • spacetime dynamics
  • mathematical foundations

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (1 paper)

Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

14 pages, 289 KB  
Article
Goedesics Completeness and Cauchy Hypersurfaces of Ricci Solitons on Pseudo-Riemannian Hypersurfaces at the Fictitious Singularity: Schwarzschild-Soliton Geometries and Generalized-Schwarzschild-Soliton Ones
by Orchidea Maria Lecian
Axioms 2025, 14(12), 896; https://doi.org/10.3390/axioms14120896 - 2 Dec 2025
Viewed by 162
Abstract
The methodology is developed here to write Ricci solitons on the newly found structure of the pseudo-spherical cylinder. The methodology is specified for Schwarzschild solitons and for Generalized-Schwarzschild solitons. Accordingly, a new classification is written for the Schwarzschild solitons and for the Generalized-Schwarzschild [...] Read more.
The methodology is developed here to write Ricci solitons on the newly found structure of the pseudo-spherical cylinder. The methodology is specified for Schwarzschild solitons and for Generalized-Schwarzschild solitons. Accordingly, a new classification is written for the Schwarzschild solitons and for the Generalized-Schwarzschild solitons. The rotational field is spelled out. The potential for a tangent vector field is used. The conditions are recalled to discriminate which submanifold of a Ricci manifold is a soliton or is an almost-Ricci soliton. It is my aim to prove that a concurrent vector field is uniquely determined after the 4-velocity vector of a Schwarzschild soliton. As a result, the analytically specified manifold, which is a spacelike submanifold of the Schwarzschild spacetime that admits Ricci solitons. The rotational killing fields are tangent to the event horizon. The conditions that are needed to match the new aspects are spelled out analytically. As a result, the two manifolds described in the work of Bardeen et al. about the requested mass of a stationary, axisymmetric solution of the Einstein Field Equations of the spacetime, which contains a blackhole surrounded with matter from the new results obtained after correcting the work of Hawking 1972 about would-be point ’beyond the conjugate point’ on the analytic continuation of the would-be geodesics: they are proven here to become the tangent manifold (which is expressed from the tangent bundle in General-Relativistic notation). The prescription here is based on one of the books of Landau et al., that the matter is not put into the metric tensor, not even in the ultra-Relativistic limit. This way, the pseudo-spherical cylinder is one implemented from the Minkowskian description and whose asymptotical limit is proven. The new methodology allows one to describe the outer region of the blackhole as one according to which the (union of the trapped) regions is one with null support. For the purpose of the present investigation, the definition of concurrent vector fields in General-Relativity is newly developed. As a further new result, the paradigm is implemented for the shrinking case, which admits as subcase the Schwarzschild manifolds and the Generalized-Schwarzschild manifolds. The Penrose 1965 Theorem is discussed for the framework outlined here; in particular, the presence of trapped hypersurfaces is discarded. The no-hair theorem can now be discussed. Full article
(This article belongs to the Special Issue Mathematical Physics in General Relativity Theory)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-1
Back to TopTop