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

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