Astrophysical properties of Weyl geometric black holes

We consider the astrophysical properties of an exact black hole solution obtained in Weyl geometric gravity theory, from the simplest conformally invariant action, constructed from the square of the Weyl scalar, and the strength of the Weyl vector only. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. In static spherical symmetry, this theory admits an exact black hole solution, which generalizes the standard Schwarzschild solution through the presence of two new terms in the metric, having a linear and a quadratic dependence on the radial coordinate. We consider in detail the motion of the massive particles and photons in this geometry, and we obtain the positions of the stable circular orbits from the extremum of the effective potential. The perihelion precession. The light deflection, the shadow, and the Shapiro effect in this Weyl-type geometry are also investigated. The quantum properties of the black hole are also considered, and the Hawking temperature and the mass loss rate due to the Hawking radiation are obtained by using both analytical and numerical methods. The obtained results may lead to the possibility of testing Weyl geometry, and its effects, at the level of the Solar System, and by using the observational properties of black holes.