https://doi.org/10.1140/epjc/s10052-022-11131-0
Regular Article - Theoretical Physics
Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
1
School of Physics, Sun Yat-Sen University, Xingang Road, 510275, Guangzhou, People’s Republic of China
2
School of Physics, Damghan University, Damghan, Iran
3
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
4
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN-HH), 077125, Bucharest, Romania
5
Astronomical Observatory, 19 Ciresilor Street, 400487, Cluj-Napoca, Romania
Received:
10
June
2022
Accepted:
11
December
2022
Published online:
26
December
2022
We consider numerical black hole solutions in the Weyl conformal geometry and its associated conformally invariant Weyl quadratic gravity. In this model, Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity after the Weyl gauge field (
) becomes massive through a Stueckelberg mechanism and it decouples. As a first step in our investigations, we write down the conformally invariant gravitational action, containing a scalar degree of freedom and the Weyl vector. The field equations are derived from the variational principle in the absence of matter. 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.
© The Author(s) 2022
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