Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor in four dimensional spacetime are obtained. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force naturally emerges from the reduced field equations and the equations of the standard Kaluza-Klein theory is demonstrated to be intrinsically contained in this model.

The Weyl-Yang gravitation gauge theory is investigated in the framework of a pure higherdimensional non-Abelian Kaluza-Klein background. We construct the dimensionally reduced field equations and energy-momentum tensors as well as the four dimensional modified Weyl-Yang+Yang-Mills theory from an arbitrary curved internal space which is a extension of our previous model. In particular, the coset space case is considered to obtain explicitly the interactions between the gravitational and the gauge fields. The results not only appear to be generalization of the well-established equations of non-Abelian theory but also contain intrinsically the generalized gravitational source term and the Lorentz force density.

A Yang-Mills-type quadratic gravity model is considered in the framework of a five-dimensional Kaluza-Klein theory. Field equations and stress-energy tensors are presented in differential forms. A five-dimensional classical Kaluza-Klein metric ansatz is investigated, which consists of a four-dimensional planefronted gravitational wave with parallel rays as its sub-metric along with a non-trivial dilaton and gauge fields. It is found that the solution is equivalent to plane-gravitational waves in terms of a spin-0 dilaton and a spin-1 photon. Some special cases are discussed, and it is shown that only the plane-electromagnetic waves with helicity-1 states carried non-zero energy-momentum.

We consider the Weyl-Yang gauge theory of gravitation in a (4 + 3)dimensional curved space-time within the scenario of the non-Abelian Kaluza-Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy-momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu-Yang ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S 3 are, respectively, included. The (anti-) dyonic solution has similar properties to those of the Reissner-Nordström-de Sitter black holes of the Einstein-Yang-Mills system. However, the cosmological constant naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model.

We study that the five dimensional theory is the transformed Weyl−Yang−Kaluza−Klein gravity. The dimensionally reduced equations of motion are derived by considering an alternative form of the master equation of the theory in the coordinate basis. The conformal transformation rules are applied for the invariants. We also discuss the possible specific cases and the new Lorentz force density term, in detail.