Charged Fluid Dynamics in Scalar-Tensor Theories of Gravity with Torsion

In scalar-tensor theories of gravity with torsion, the gravitational field is described in terms of a symmetric metric tensor g, a metriccompatible connection ∇ with torsion, and a scalar field φ. The main aim is to explore an interaction of a charged perfect fluid and a scalar field φ in a background electromagnetic and gravitational field described by {g, ∇, φ}. The interaction is based on an action functional SC of a charged perfect fluid that is invariant under global conformal rescalings. Using a variational principle, we obtain equations of motion for the charged perfect fluid. Moreover, we verify that these equations of motion are equivalent to the gauge identities obtained from the invariance of an action functional under spacetime dffeomorphisms and a local U(1) gauge group. 1 Action Functionals of Charged Perfect Fluids In Brans-Dicke theory [1] a direct interaction between the Brans-Dicke scalar field and matter is often said to violate the weak equivalence principle [7]. However, as Dirac [4] has shown one may consider gravity in a Weyl geometry which naturally induces such interactions. But little exploration has been made of gravitational scalar field interactions in a Cartan geometry. Dereli and Tucker [3] have noted that the motion of an electrically neutral spinless particle in the background geometry of Dirac’s theory can also be reformulated in terms of an autoparallel of a Cartan geometry with torsion determined by the gradient of the Brans-Dicke scalar field [2]. In this note, we examine the motion of a relativistic charged fluid in a background Cartan geometry determined by a scalar field. We shall motivate a particular coupling of such a field to the fluid and derive the equations of motion from an action principle. Institute of Physics, Academia Sinica, Taipei 115, Taiwan, Republic of China(email : [email protected]) Department of Physics, Lancaster University, UK (email : [email protected])