f(R) gravity is examined in the context of a five-dimensional Kaluza-Klein theory with degenerate metric. In this theory electromagnetism is described by two vector fields, and there is a reflection symmetry between them which unifies them with gravitation. For matter, it is shown how the Lagrangian may be any function and still generate the same equations of motion, provided that some simple conditions are satisfied. The field equations are derived, and it is found that f(R) gravity is not consistent with the reflection symmetry.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Searight, T.P.: On degenerate metrics, dark matter and unification. J. Math. Phys. 58, 122502 (2017)
Searight, T.P.: Completing the dark matter solutions in degenerate Kaluza-Klein theory. J. Math. Phys. 60, 042501 (2019)
Starobinsky, A.A.: A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99–102 (1980)
De Felice, A., Tsujikawa, S.: f(R) theories. Living Rev. Relativ. 13, 3 (2010)
Sotiriou, T.P., Faraoni, V.: f(R) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010)
Chiba, T.: 1/R gravity and scalar-tensor gravity. Phys. Lett. B 575, 1–3 (2003)
Carroll, S.M., De Felice, A., Duvvuri, V., Easson, D.A., Trodden, M., Turner, M.S.: The cosmology of generalized modified gravity models. Phys. Rev. D 71, 063513 (2005)
Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: f(R, T) gravity. Phys. Rev. D 84, 024020 (2011)
Amendola, L., Polarski, D., Tsujikawa, S.: Are f(R) models cosmologically viable? Phys. Rev. Lett. 98, 131302 (2007)
Olmo, G.J.: Limit to general relativity in f(R) theories of gravity. Phys. Rev. D 75, 023511 (2007)
Jana, S., Mohanty, S.: Constraints on f(R) theories of gravity from GW170817. Phys. Rev. D 99, 044056 (2019)
Corda, C.: Interferometric detection of gravitational waves: the definitive test for General Relativity. Int. J. Mod. Phys. D 18, 2275–2282 (2009)
Berry, C.P.L., Gair, J.R.: Linearized f(R) gravity: gravitational radiation and Solar System tests. Phys. Rev. D 83, 104022 (2011)
Habib Mazharimousavi, S., Halilsoy, M., Tahamtan, T.: Solutions for f(R) gravity coupled with electromagnetic field. Eur. Phys. J. C 72, 1851 (2012)
Ayón-Beato, E., García, A.: The Bardeen Model as a Nonlinear Magnetic Monopole. Phys. Lett. B 493, 149–152 (2000)
Hollenstein, L., Lobo, F.S.N.: Exact solutions of f(R) gravity coupled to nonlinear electrodynamics. Phys. Rev. D 78, 124007 (2008)
Rodrigues, M.E., Junior, E.L.B., Marques, G.T., Zanchin, V.T.: Regular black holes in f(R) gravity coupled to nonlinear electrodynamics. Phys. Rev. D 94, 024062 (2016)
Kruglov, S.I.: Inflation of universe due to nonlinear electrodynamics. Int. J. Mod. Phys. A 32, 1750071 (2017)
Kruglov, S.I.: Nonlinear electrodynamics and magnetic back holes. Ann. Phys. (Berlin) 529, 1700073 (2017)
Bronnikov, K.A.: Nonlinear electrodynamics, regular black holes and wormholes. Int. J. Mod. Phys. D 27, 1841005 (2018)
Kuang, X.-M., Liu, B., Övgün, A.: Nonlinear electrodynamics AdS black hole and related phenomena in the extended thermodynamics. Eur. Phys. J. C 78, 840 (2018)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Searight, T.P. f(R) Gravity in a Kaluza–Klein Theory with Degenerate Metric. Found Phys (2020). https://doi.org/10.1007/s10701-020-00329-5
- f(R) gravity
- Kaluza–Klein theory
- Degenerate metric
- Nonlinear electrodynamics