Massive Vector Meson Interacting with the Gravitational Field. I. General Formalism

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Abstract
Starting from the covariant field equations for a vector meson, the energy-momentum tensor entering in Einstein's field equations is derived. It is shown that its most general algebraic form involves two vector fields and two scalars. Specifying the formalism to the special cases for which the fields are either parallel or perpendicular to each other, it is found that the vector field cannot be described in terms of a perfect fluid involving only density and pressure, but includes an additional term involving the stresses. The conservation laws are given, which, in addition to the ones of relativistic hydrodynamics, also include the ones describing the streaming of the vector field.

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