Class. Quantum Grav. 7 (1990) 1109-1115. Printed in the UK Kaluza-Klein reduction of generalised theories of gravity and non-minimal gauge couplings T DerelM and G UGolukO lnstitut fur Theoretische Physik, Universitat Karlsruhe, D-7500 Karlsruhe 1, Federal Republic of Germany Received 25 May 1989, in final form 19 January 1990 Abstract. The Kaluza-Klein reduction of a generalised theory of gravity in D = 5 dimensions is given. The form of the interactions among the gravitational, electromagnetic and massless scalar fields in four dimensional spacetime is exhibited. 1. Introduction The gravitational fields in four-dimensional spacetime are described in terms of a Lorentzian metric tensor g and an independent metric compatible connection w that is a rule for parallelly transporting tensorial quantities along curves in spacetime. The field equations satisfied by g and w are obtained from a locally Lorentz invariant action 1 L(g, w) M4 by a well defined variational principle. Einstein gravitational theory is based on the single non-trivial curvature invariant linear in curvature components. Thus we consider the Einstein-Hilbert 4-action where K~ = 8rG/ c3 is the universal gravitational constant. Independent connection variations of Z, imply that the connection is Levi-Civita. Then the source-free Einstein equations obtained by coframe variations of Io involve at most second-order partial derivatives of the components of the metric tensor. Conceptually the simplest way to generalise Einstein theory is to write down 4-actions using higher order curvature invariants. A popular generalised theory of gravity is described by the 4-action [ 1,2] 1, = k Rah A *Rah 1M4 t A von Humbold-Foundation Fellow. $ Permanent address: Department of Physics, Faculty of Sciences, Ankara University, Ankara, Turkey. B Permanent address: Department of Physics, Middle East Technical University, Ankara, Turkey. 0264-9381/90/071109+07$03.50 @ 1990 IOP Publishing Ltd 1109