Black hole solutions in Weyl geometric gravity

We consider numerical black hole solutions in the linear representation of the conformally invariant Weyl quadratic gravity. By adopting a static spherically symmetric geometry, the vacuum field equations for the gravitational, scalar, and Weyl fields are obtained. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components, indicating the existence of the singularity in the metric. Several models, corresponding to different functional forms of the Weyl vector, are considered. An exact black hole model, corresponding to a Weyl vector having only a radial spacelike component, is also obtained. The thermodynamic properties of the Weyl geometric type black holes (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also analyzed in detail.