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

Abstract

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 (${\omega }_{\mu }$) 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.

29 pages, 13 figures, accepted for publication in EPJC

References in corpus (33)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Resummation of Massive Gravity
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Conformal Symmetry and the Standard Model
• Thin accretion disks in stationary axisymmetric wormhole spacetimes
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Electromagnetic signatures of thin accretion disks in wormhole geometries
• Testing Hořava-Lifshitz gravity using thin accretion disk properties
• Solution to the ghost problem in fourth order derivative theories
• New perspective for black hole thermodynamics in Gauss-Bonnet-Born-Infeld massive gravity
• Iron K$\alpha$ line of Kerr black holes with scalar hair
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Black Holes in $f(T,B)$ Gravity: Exact and Perturbed Solutions
• Gauging scale symmetry and inflation: Weyl versus Palatini gravity
• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Thin accretion disk signatures of slowly rotating black holes in Hořava gravity
• Analytical study of higher-order ring images of accretion disk around black hole
• Standard Model in Weyl conformal geometry
• Dilatonic black holes in gravity's rainbow with a nonlinear source: the effects of thermal fluctuations
• Jacobi stability of the vacuum in the static spherically symmetric brane world models
• Testing the Kerr metric with the iron line and the KRZ parametrization
• Black hole solutions in scalar-tensor symmetric teleparallel gravity
• Black hole solutions in mimetic Born-Infeld gravity
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Thin accretion discs around spherically symmetric configurations with nonlinear scalar fields
• A Weyl-Dirac Cosmological Model with DM and DE
• Thin accretion disks around cold Bose-Einstein Condensate stars
• Distinguishing Brans-Dicke-Kerr type naked singularities and black holes with their thin disk electromagnetic radiation properties
• Lee-Wick Black Holes
• Black hole solutions in functional extensions of Born-Infeld gravity
• Black hole and naked singularity geometries supported by three-form fields
• Spatially homogeneous black hole solutions in $z=4$ Hořava-Lifshitz gravity in $(4+1)$ dimensions with Nil geometry and $H^2\times R$ horizons

Cited by in corpus (21)

• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• New black hole solutions with a dynamical traceless nonmetricity tensor in Metric-Affine Gravity
• Compact stellar structures in Weyl geometric gravity
• Inflation in Weyl-invariant Einstein-Cartan gravity
• Einstein-Proca theory from the Einstein-Cartan formulation
• Cosmological implications of the Weyl geometric gravity theory
• Weyl geometric effects on the propagation of light in gravitational fields
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian Boundary
• Algebraic classification of the gravitational field in Weyl-Cartan space-times
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Mimetic Weyl geometric gravity
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• Observational tests of the conformal osculating Barthel-Kropina cosmological model
• Algebraic classification of the gravitational field in general metric-affine geometries
• Revisiting local-scale invariant gravitational theory
• Black hole shadows in nonminimally coupled Weyl connection gravity
• Nonconformally Ricci-flat instantons in Conformal Gravity with and without nonlinear matter fields
• Yano-Schrödinger Hyperfluid: Cosmological Implications
• The Weyl Geometric Gravity black hole in light of the Solar System tests