S. E. Stepanov, “On group-theoretic approach to study Einstein's and Maxwell's equations”, TMF, 111:1 (1997), 32–43; Theoret. and Math. Phys., 111:1 (1997), 419

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 111, Number 1, Pages 32–43
DOI: https://doi.org/10.4213/tmf988 (Mi tmf988)

This article is cited in 15 scientific papers (total in 15 papers)

On group-theoretic approach to study Einstein's and Maxwell's equations

S. E. Stepanov

Vladimir State Pedagogical University

Full-text PDF (248 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf988

Abstract: Basing on the classical problem of the representation theory of the orthogonal group about decomposition of the tensor product of representations on irreducible components the partial classification of Einstein's equations is obtained. A new class of Maxwell's equations of relativistic electrodynamics is singled out and studied. The pointwise irreducible decompositions of the energy-momentum tensor as well as the tensor of the electro-magnetic field are established and a physical interpretation of the corresponding components is given.

Received: 14.03.1996

English version:
Theoretical and Mathematical Physics, 1997, Volume 111, Issue 1, Pages 419–427
DOI: https://doi.org/10.1007/BF02634197

Bibliographic databases:

Language: Russian

Citation: S. E. Stepanov, “On group-theoretic approach to study Einstein's and Maxwell's equations”, TMF, 111:1 (1997), 32–43; Theoret. and Math. Phys., 111:1 (1997), 419–427

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\pages 419--427

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Linking options:

https://www.mathnet.ru/eng/tmf988

https://doi.org/10.4213/tmf988

https://www.mathnet.ru/eng/tmf/v111/i1/p32

This publication is cited in the following 15 articles:

S.E. Stepanov, I. I. Tsyganok, “Pointwise orthogonal splitting of the space of TT-tensors”, Differ. Geom. Mnogoobr. Figur, 2023, no. 54(2), 45
Nazarenko O., Kadievskaya I., Wright H., “On the Deformation With the Special Type of Stress Tensor”, AIP Conference Proceedings, 2302, ed. Todorov M., Amer Inst Physics, 2020, 040006
Josef Mikeš et al., Differential Geometry of Special Mappings, 2019
Josef Mikeš et al., Differential Geometry of Special Mappings, 2019
Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566
Stepanov S., Mikes J., “Seven Invariant Classes of the Einstein Equations and Projective Mappings”, XX International Fall Workshop on Geometry and Physics, AIP Conference Proceedings, 1460, eds. Linan M., Barbero F., DeDiego D., Amer Inst Physics, 2012, 221–225
T. V. Zudina, S. E. Stepanov, I. G. Shandra, “Equiaffine mappings”, Russian Math. (Iz. VUZ), 51:8 (2007), 25–32
T. V. Zudina, S. E. Stepanov, “On the classification of equivolume mappings of pseudo-Riemannian manifolds”, Russian Math. (Iz. VUZ), 50:8 (2006), 17–25
S. E. Stepanov, “Vanishing theorems in affine, Riemannian, and Lorenz geometries”, J. Math. Sci., 141:1 (2007), 929–964
S. E. Stepanov, I. G. Shandra, “Garmonic diffeomorphisms of manifolds”, St. Petersburg Math. J., 16:2 (2005), 401–412
S. E. Stepanov, “The Killing–Yano Tensor”, Theoret. and Math. Phys., 134:3 (2003), 333–338
Stepanov, SE, “On conformal Killing 2-form of the electromagnetic field”, Journal of Geometry and Physics, 33:3–4 (2000), 191
S. E. Stepanov, “An analytic method in general relativity”, Theoret. and Math. Phys., 122:3 (2000), 402–414
V. A. Astapenko, L. A. Bureeva, V. S. Lisitsa, “Classical and quantum theories of the polarization bremsstrahlung in the local electron density model”, J. Exp. Theor. Phys., 90:3 (2000), 434
V. A. Astapenko, “Polarization-interference effects in the bremsstrahlung of quasiclassical electrons on ions with a core”, J. Exp. Theor. Phys., 88:5 (1999), 889

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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