Аннотация:
Описан альтернативный формализм теории тяготения Эйнштейна. Роль динамических переменных играет набор из десяти векторных полей $f_{\mu}^{A}$, $A=1,\dots,10$. Метрика является композитной переменной, $g_{\mu\nu}=f_{\mu}^{A}f_{\nu}^{A}$. Предложенная схема может дать дальнейшее развитие теории тяготения, в котором теория Эйнштейна будет играть роль эффективной теории, и константа Ньютона появится посредством введения аномальной функции Грина.
Ключевые слова:
теория тяготения Эйнштейна, векторные поля, гамильтонова формулировка.
С. А. Пастон, “Темная материя как гравитационный эффект в подходе теории вложения”, ТМФ, 216:3 (2023), 559–576; S. A. Paston, “Dark matter as a gravitational effect in the embedding theory approach”, Theoret. and Math. Phys., 216:3 (2023), 1382–1395
S. A. Paston, T. I. Zaitseva, “Canonical Formulation of Embedding Gravity in a Form of General Relativity with Dark Matter”, Gravit. Cosmol., 29:2 (2023), 153
Stanislav Kuptsov, Mikhail Ioffe, Sergey Manida, Sergey Paston, “Weak Field Limit for Embedding Gravity”, Universe, 8:12 (2022), 635
Paston S.A., “Dark Matter From Non-Relativistic Embedding Gravity”, Mod. Phys. Lett. A, 36:15 (2021), 2150101
S. S. Kuptsov, S. A. Paston, “Investigation of Faddeev variant of embedding theory”, J. Phys.: Conf. Ser., 2103:1 (2021), 012003
Ilin R., Paston S., “Energy-Momentum Pseudotensor and Superpotential For Generally Covariant Theories of Gravity of General Form”, Universe, 6:10 (2020), 173
Paston S., “Non-Relativistic Limit of Embedding Gravity as General Relativity With Dark Matter”, Universe, 6:10 (2020), 163
Kapustin A.D., Ioffe V M., Paston S.A., “Explicit Isometric Embeddings of Collapsing Dust Ball”, Class. Quantum Gravity, 37:7 (2020), 075019
Paston S., Semenova E., Sheykin A., “Canonical Description For Formulation of Embedding Gravity as a Field Theory in a Flat Spacetime”, Symmetry-Basel, 12:5 (2020)
A A Sheykin, M V Markov, Ya A Fedulov, S A Paston, “Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications”, J. Phys.: Conf. Ser., 1697:1 (2020), 012077
A D Kapustin, S A Paston, “Explicit isometric embeddings of black holes geometry with non-singular matter distribution”, J. Phys.: Conf. Ser., 1697:1 (2020), 012082
Sheykin A., Solovyev D., Paston S., “Global Embeddings of Btz and Schwarzschild-Ads Type Black Holes in a Flat Space”, Symmetry-Basel, 11:7 (2019), 841
Grad D.A., Ilin R.V., Paston S.A., Sheykin A.A., “Gravitational Energy in the Framework of Embedding and Splitting Theories”, Int. J. Mod. Phys. D, 27:2 (2018), 1750188
Paston S.A., Sheykin A.A., “Embedding Theory as New Geometrical Mimetic Gravity”, Eur. Phys. J. C, 78:12 (2018), 989
Paston S.A., Semenova E.N., Franke V.A., Sheykin A.A., “Algebra of implicitly defined constraints for gravity as the general form of embedding theory”, Gravit. Cosmol., 23:1 (2017), 1–7
Mielke E.W., “Color Geometrodynamics”: Mielke, EW, Geometrodynamics of Gauge Fields: on the Geometry of Yang-Mills and Gravitational Gauge Theories, 2Nd Edition, Mathematical Physics Studies, Springer International Publishing Ag, 2017, 329–345
Khatsymovsky V.M., “First-Order Discrete Faddeev Gravity At Strongly Varying Fields”, Mod. Phys. Lett. A, 32:35 (2017), 1750181
Khatsymovsky V.M., “Spectrum of area in the Faddeev formulation of gravity”, Mod. Phys. Lett. A, 31:19 (2016), 1650114
Khatsymovsky V.M., “First-Order Minisuperspace Model For the Faddeev Formulation of Gravity”, Mod. Phys. Lett. A, 30:32 (2015), 1550174