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f(R) Gravity in a Kaluza–Klein Theory with Degenerate Metric

Abstract

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.

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Correspondence to Trevor P. Searight.

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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

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Keywords

  • f(R) gravity
  • Kaluza–Klein theory
  • Degenerate metric
  • Nonlinear electrodynamics