Black hole solutions in the quadratic Weyl conformal geometric theory of gravity

We consider numerical black hole solutions inthe Weyl conformal geometry and its associated conformallyinvariant Weyl quadratic gravity. In this model, Einstein grav-ity (with a positive cosmological constant) is recovered in thespontaneously broken phase of Weyl gravity after the Weylgauge field (omega mu) becomes massive through a Stueckelbergmechanism and it decouples. As a first step in our investiga-tions, we write down the conformally invariant gravitationalaction, containing a scalar degree of freedom and the Weylvector. The field equations are derived from the variationalprinciple in the absence of matter. By adopting a static spher-ically symmetric geometry, the vacuum field equations forthe gravitational, scalar, and Weyl fields are obtained. Afterreformulating the field equations in a dimensionless form,and by introducing a suitable independent radial coordinate,we obtain their solutions numerically. We detect the forma-tion of a black hole from the presence of a Killing horizon forthe timelike Killing vector in the metric tensor components,indicating the existence of the singularity in the metric. Sev-eral models corresponding to different functional forms ofthe Weyl vector are considered. An exact black hole modelcorresponding to a Weyl vector having only a radial spacelikecomponent is also obtained. The thermodynamic propertiesof the Weyl geometric type black holes (horizon temperature,specific heat, entropy, and evaporation time due to Hawkingluminosity) are also analyzed in detail.

Automated summary

We consider the numerical solutions of black holes in the Weyl conformal geometry and its associated conformally invariant Weyl quadratic gravity. By reformulating the field equations and using suitable coordinates, we numerically solve these equations and observe the formation of black holes.