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Symmetry
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New Solutions of Einstein Equations in Spherical Symmetry
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New Solutions of Einstein Equations in Spherical Symmetry

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

Deadline for manuscript submissions: closed (10 March 2021) | Viewed by 6694

Special Issue Editors

Prof. Salvatore Capozziello

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Guest Editor
Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Napoli, Italy
Interests: extended theories of gravity; exact solutions in general relativity and cosmology: quantum field in curved spacetime; quantum cosmology
Dr. Orlando Luongo

E-Mail Website
Guest Editor
Department of Physics, University of Camerino, 62032 Camerino, Italy
Interests: theoretical physics; cosmology; quantum field theories; relativistic quantum information
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Roberto Giambò

E-Mail Website
Guest Editor
Scuola di Scienze e Tecnologie, Università di Camerino, Camerino, Italy
Interests: gravitational collapse; singularity formation; exact solutions in general relativity; qualitative behavior of cosmological solutions

Special Issue Information

Dear Colleagues,
    As a purely mathematical theory, Einstein's Relativity predicts many models, whose properties can arouse interest in view of experimental proof of their actual validity. In the search for exact solutions to Einstein's equations, and related field equations coming from other theories of gravity, spherical solutions have obviously played a central role from the beginning. Despite its inadequacy in describing a phenomenon of great importance and topicality, such as the emission of gravitational waves, spherical symmetry represents a rich training ground of relatively simple mathematical models, which can, however, show many central features of any theory of gravitation, such as gravitational collapse, the onset of horizons, and the formation of singularities. Furthermore, it is well known that the principles underlying relativistic cosmology lead us to consider the evolution of the universe in a spherical framework.
    In this Special Issue of Symmetry, we wish to host contributions that illustrate the richness of Einstein's theory, through the presentation of new spherical solutions or through an original reinterpretation of the physical meaning of solutions already known in the literature, possibly also in the context of extended theories of gravity. Experts in the theory of Relativity are cordially invited to contribute their work on the topics indicated above.

Prof. Salvatore Capozziello
Prof. Orlando Luongo
Prof. Roberto Giambò
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. 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.

Keywords

  • Spherical symmetry
  • Cosmological solutions
  • Gravitational collapse
  • Extended theories of gravity
  • Black holes
  • Singularities
  • Horizons
  • Dark energy
  • Dark matter

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Published Papers (2 papers)

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Research

24 pages, 355 KiB  
Article
Metric-Affine Geometries with Spherical Symmetry
by Manuel Hohmann
Symmetry 2020, 12(3), 453; https://doi.org/10.3390/sym12030453 - 12 Mar 2020
Cited by 45 | Viewed by 2887
Abstract
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, [...] Read more.
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the tetrad/spin connection formulation, and show its characteristic properties: torsion, curvature and nonmetricity. We then use these properties to derive a classification of all possible subclasses of spherically symmetric metric-affine geometries, depending on which of the aforementioned quantities are vanishing or non-vanishing. We discuss both the cases of the pure rotation group SO ( 3 ) , which has been previously studied in the literature, and extend these previous results to the full orthogonal group O ( 3 ) , which also includes reflections. As an example for a potential physical application of the results we present here, we study circular orbits arising from autoparallel motion. Finally, we mention how these results can be extended to cosmological symmetry. Full article
(This article belongs to the Special Issue New Solutions of Einstein Equations in Spherical Symmetry)
8 pages, 231 KiB  
Article
The Erez–Rosen Solution Versus the Hartle–Thorne Solution
by Kuantay Boshkayev, Hernando Quevedo, Gulmira Nurbakyt, Algis Malybayev and Ainur Urazalina
Symmetry 2019, 11(10), 1324; https://doi.org/10.3390/sym11101324 - 22 Oct 2019
Cited by 4 | Viewed by 3023
Abstract
In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe [...] Read more.
In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez–Rosen and the Hartle–Thorne solutions are particular solutions of a more general solution, the Zipoy–Voorhees transformation is applied to the exact Erez–Rosen metric in order to obtain a generalized solution in terms of the Zipoy–Voorhees parameter δ = 1 + s q . The Geroch–Hansen multipole moments of the generalized Erez–Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass m, quadrupole q and Zipoy–Voorhees δ parameters. The coordinate transformations between the metrics are found in the approximation of ∼q. It is shown that the Zipoy–Voorhees parameter is equal to δ = 1 − q with s = − 1 . This result is in agreement with previous results in the literature. Full article
(This article belongs to the Special Issue New Solutions of Einstein Equations in Spherical Symmetry)
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