Boyut indirgemesi ve varyasyon işlemlerinin ikinci dereceden eğrilikli ve kaluza-kleın anzatslı modelde uyumluluğu

The Kaluza-Klein theory is investigated for a 5D quadratic curvature Lagrangian. In order to obtain the field equations in the actual 4D spacetime, there are two different approaches composed of two successive applications to be implemented to the 5D action. Either one applies the least action principle with respect to the 5D variables and then uses the dimensional reduction mechanism, or changes the order by first reducing the action and then takes the variations with respect to the constituent fields of the theory. In this work, the field equations are obtained from the reduced form of the action and the results are compared with those obtained by the reverse procedure. The differences between these two procedures along with their outcomes are presented in detail, and their origins are explained.