Dynamics of test bodies in scalar-tensor theory and equivalence principle

Abstract

How do test bodies move in scalar-tensor theories of gravitation ? We provide an answer to this question on the basis of a unified multipolar scheme. In particular, we give the explicit equations of motion for pointlike, as well as spinning test bodies, thus extending the well-known general relativistic results of Mathisson, Papapetrou, and Dixon to scalar-tensor theories of gravity. We demonstrate the validity of the equivalence principle for test bodies.We study a class of scalar-tensor theories (along the lines of [6]) with the actionThis extends the Brans-Dicke theory [28,29] to the case with a multiplet of scalar fields ϕ A (capital indices A, B, C = 1, . . . , N label the components of the multiplet). Here κ = 8πG/c 4 is Einstein's gravitational constant andThe Lagrangian L m (ψ, ∂ψ, J g ij ) depends on the matter fields ψ.The metric J g ij determines angles and intervals in the Jordan reference frame.The Riemannian curvature scalar R( J g ) is constructed from the Jordan metric. With the help of the conformal transformation J