Compatibility of the dimensional reduction and variation procedures for a quadratic curvature model with a Kaluza–Klein Ansatz


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Başkal S., ÇELİK S.

General Relativity and Gravitation, vol.54, no.10, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 10
  • Publication Date: 2022
  • Doi Number: 10.1007/s10714-022-03029-9
  • Journal Name: General Relativity and Gravitation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Keywords: Kaluza-Klein theory, Dimensional reduction, Quadratic curvature, Non-minimal couplings, GRAVITATIONAL-FIELD, GRAVITY, PHOTON
  • Middle East Technical University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.The introduction of extra dimensions is an invaluable strategy for the unification of gravity with other physical fields. Nevertheless, the matter in hand is to be eventually reduced to the actual 4D spacetime. The Kaluza–Klein theory is no exception to this well-known scheme. There are two procedures to obtain the field equations from a higher dimensional action. One can either take the variation of the effective action in that higher dimension and then reduce the resulting equations or reduce the higher dimensional action to the actual 4D and henceforward take the variations with respect to the constituent fields of the theory. Here, for the case of a quadratic curvature model with a Kaluza–Klein ansatz the field equations are obtained from the reduced action and compatibility of these two procedures is discussed in detail.