{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:17Z","timestamp":1740165257752,"version":"3.37.3"},"reference-count":9,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,3,29]],"date-time":"2021-03-29T00:00:00Z","timestamp":1616976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"It was shown that from the mathematical physics equations that are composed of the conservation laws equations for energy, momentum, angular momentum, and mass and describe material media such as thermodynamical, gas-dynamical, cosmic, and others, it follows the evolutionary relation that possesses the properties of field theory equations. The evolutionary relation, which is based on conservation laws, unites the field theory equations, reveals their internal connection, and discloses the properties, which are common for all equations of field theory. The correspondence between the equations of field theory and evolutionary relation physics indicates that the equations of field theory are related to the equations of mathematical physics. This can reveal the fundamentals of field theory. These results are obtained using skew-symmetric differential forms describing conservation laws on which the equations of mathematical physics and equations of field theory are based. In this paper, the Einstein equation will be investigated by application of skew-symmetric differential forms.<\/jats:p>","DOI":"10.3390\/axioms10020046","type":"journal-article","created":{"date-parts":[[2021,3,29]],"date-time":"2021-03-29T20:01:57Z","timestamp":1617048117000},"page":"46","source":"Crossref","is-referenced-by-count":4,"title":["Evolutionary Relation of Mathematical Physics Equations Evolutionary Relation as Foundation of Field Theory Interpretation of the Einstein Equation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4726-927X","authenticated-orcid":false,"given":"Ludmila","family":"Petrova","sequence":"first","affiliation":[{"name":"Department of Computational Mathematics and Cybernetics, Moscow State University, 119991 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,29]]},"reference":[{"key":"ref_1","unstructured":"Petrova, L.I. (2021, March 22). Exterior and Evolutionary Skew-Symmetric Differential Forms and Their Role in Mathematical Physics. Available online: http:\/\/arxiv.org\/pdf\/math-ph\/0310050v1.pdf."},{"key":"ref_2","unstructured":"Clark, J.F., and Machesney, M. (1964). The Dynamics of Real Gases, Butterworths."},{"key":"ref_3","unstructured":"Tolman, R.C. (1969). Relativity, Thermodynamics, and Cosmology, Clarendon Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"78","DOI":"10.5539\/jmr.v4n3p78","article-title":"Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor","volume":"4","author":"Petrova","year":"2012","journal-title":"J. Math. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.4236\/jamp.2020.89144","article-title":"Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)","volume":"8","author":"Petrova","year":"2020","journal-title":"J. Appl. Math. Phys."},{"key":"ref_6","unstructured":"Tonnelat, M.A. (1959). Les Principles de la Theorie Electromagnetique et la Relativite, Masson."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"012032","DOI":"10.1088\/1742-6596\/1557\/1\/012032","article-title":"Formatting Physical Fields and Pseudometric Manifolds. The Dark Matter","volume":"1557","author":"Petrova","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_8","unstructured":"Einstein, A. (1953). The Meaning of Relativity, Princeton University Press."},{"key":"ref_9","unstructured":"Weinberg, S. (1972). Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity, Wiley & Sons, Inc."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T10:19:46Z","timestamp":1720606786000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,29]]},"references-count":9,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020046"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020046","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,3,29]]}}}