Gravitational interaction of a vector field with account of the nonmetricity of space-time

Abstract

The gravitational interaction of a vector field is investigated in a space with the nonmetricity described by the Weyl vector. The analogue of the Coulomb law for the electrostatic field of a point charge is found in such a space. It is shown that taking account of the nonmetricity of space-time leads to the appearance of a nonlinearity in a massive vector field, resulting in the sine-Gordon and shine-Gordon equations. The screening of the vector-field mass as a consequence of its interaction with the nonmetricity is clarified. The solution for the Reissner-Nordström problem in a Weyl space is obtained, which asymptotically coincides with the solution of the same problem in general relativity, but nowhere does it possess singularities apart from at the origin. The obtained results show that it is reasonable to take account of the nonmetricity when describing the gravitational interaction of a vector field.