Weyl geometric gravity black holes in light of the Solar System tests

Weyl geometric gravity theory, in which gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a scalar–vector–tensor representation, obtained by introducing an auxiliary scalar field, and can therefore be reformulated as a scalar–vector–tensor theory in a Riemann space in the presence of a non-minimal coupling between the Ricci scalar and the scalar field. By assuming that the Weyl vector has only a radial component, an exact spherically symmetric vacuum solution of the field equations can be obtained, depending on three integration constants. As compared to the Schwarzschild solution, the Weyl geometric gravity solution contains two new terms, linear and quadratic, in the radial coordinate, respectively. We consider the possibility of testing and obtaining observational restrictions on the Weyl geometric gravity black hole at the scale of the Solar System, by considering six classical tests of general relativity (gravitational redshift, the Eötvös parameter and the universality of free fall, the Nordtvedt effect, the planetary perihelion precession, the deflection of light by a compact object, and the radar echo delay effect) for an exact spherically symmetric black hole solution of the Weyl geometric gravity. These gravitational effects can be fully explained, and are consistent with the vacuum solution of the Weyl geometric gravity. Moreover, the study of the classical general relativistic tests also allows us to constrain the free parameter of the solution.