Weyl Gravity Research Articles

Quasinormal modes of the Mannheim–Kazanas black holes

Abstract A spherically symmetric black hole solution in the conformal Weyl gravity was found by Mannheim and Kazanas in 1988. While the quasinormal modes (QNMs) of these black holes have been considered in a few works, here we complement these studies by considering in detail the regime of vanishing cosmological constant and negative values of the Weyl parameter for which we find quasinormal frequencies for scalar, Dirac and electromagnetic perturbations with the time-domain integration and WKB methods. In particular, we derive the compact and remarkably accurate analytic formula for the frequencies in the form of expansion in terms of the inverse multipole number. Comparison with the time-domain integration shows that the 6th order WKB method with the Padé approximants is quite accurate, unless the black hole is in the near extreme state.

Effectiveness of Weyl gravity in probing quantum corrections to AdS black holes

Computing leading higher curvature contributions to thermodynamic quantities of AdS black hole is drastically simplified once the higher curvature terms are expressed in terms of powers of Weyl tensor by applying proper field redefinitions, avoiding the usual complications caused by higher derivative Gibbons-Hawking-York term or surface counterterms. We establish the method by computing the Euclidean action of general rotating anti–de Sitter (AdS) black holes in five-dimensional quadratic curvature theories with or without supersymmetry and verifying the results numerically. Our result is the state of the art for charged rotating AdS black holes in five-dimensional minimal gauged supergravity including corrections from all three supersymmetric curvature squared terms. Our approach facilitates precision tests in the AdS/CFT correspondence and should be applicable in diverse dimensions. Published by the American Physical Society 2024

Generalized Gibbons-Werner method for stationary spacetimes

The Gibbons-Werner (GW) method is a powerful approach in studying the gravitational deflection of particles moving in curved spacetimes. The application of the Gauss-Bonnet theorem (GBT) to integral regions constructed in a two-dimensional manifold enables the deflection angle to be expressed and calculated from the perspective of geometry. However, different techniques are required for different scenarios in the practical implementation which leads to different GW methods. For the GW method for stationary axially symmetric (SAS) spacetimes, we identify two problems: (a) the integral region is generally infinite, which is ill-defined for some asymptotically nonflat spacetimes whose metric possesses singular behavior, and (b) the intricate double and single integrals bring about complicated calculation, especially for highly accurate results and complex spacetimes. To address these issues, a generalized GW method is proposed in which the infinite region is replaced by a flexible region to avoid the singularity, and a simplified formula involving only a single integral of a simple integrand is derived by discovering a significant relationship between the integrals in conventional methods. Our method provides a comprehensive framework for describing the GW method for various scenarios. Additionally, the generalized GW method and simplified calculation formula are applied to three different kinds of spacetimes — Kerr spacetime, Kerr-like black hole in bumblebee gravity, and rotating solution in conformal Weyl gravity. The first two cases have been previously computed by other researchers, affirming the effectiveness and superiority of our approach. Remarkably, the third case is newly examined, yielding a innovative result for the first time.

Time-dependent wormhole solutions in conformal Weyl gravity

Time-dependent wormhole solutions in conformal Weyl gravity

Gravitational lens on a static optical constant-curvature background: Its application to the Weyl gravity model

Gravitational lens on a static optical constant-curvature background: Its application to the Weyl gravity model

Weyl gravity in covariant hamiltonian formalism

Abstract We find covariant canonical formalism for Weyl invariant gravity. We discuss constraint structure of this theory and its gauge fixed form and we argue that it corresponds to unimodular gravity.

Stability of Schwarzshild black holes in quadratic gravitywith Weyl curvature domination

We study the linear stability of static and spherically symmetric (SSS)black holes (BHs) in the presence of a Weyl-squared curvaturebesides an Einstein-Hilbert term in the action.In this theory, there is always an exact Schwarzschild BHirrespective of the Weyl coupling constant α,with the appearance of a non-Schwarzschild solutionfor a particular range of the coupling oforder |α| ≈ r h 2 (where r h isthe horizon radius).On the SSS background, we show that the propagating degreesof freedom (DOFs) are three in the odd-parity sector and fourin the even-parity sector. Since the number of total seven DOFs coincides with those on the Minkowski and isotropic cosmological backgrounds, the Weyl gravity does not pose a strong coupling problem associated with the vanishing kinetic term of dynamical perturbations.The odd-parity perturbations possess at least one ghost mode,but the propagation speeds of all three dynamical modesare luminal.In the even-parity sector, our analysis, based on the WKB approximation, shows that, besides the appearance of at least one ghost mode, the Schwarzschild solution is prone to both radial and angular Laplacian instabilities of several dynamical perturbations for the Weyl coupling in the range |α| ≫ r h 2.For large radial and angular momentum modes, the time scales of such instabilities are much shorter than the horizon distance r h divided by the speed of light.In the coupling regime |α|≲ r h 2, the WKB approximation does not hold any longer, and a different analysis should be performedif one wants to state the stability of both the Schwarzschild andnon-Schwarzschild BH solutions in this range of model parameters.

Projective transformations in metric-affine and Weylian geometries

We discuss generalizations of the notions of projective transformations acting on affine model of Riemann–Cartan and Riemann–Cartan–Weyl gravity which preserve the projective structure of the light-cones. We show how the invariance under some projective transformations can be used to recast a Riemann–Cartan–Weyl geometry either as a model in which the role of the Weyl gauge potential is played by the torsion vector, which we call torsion-gauging, or as a model with traditional Weyl (conformal) invariance.

Covariant action for conformal higher spin gravity

Conformal higher spin (HS) gravity is a HS extension of Weyl gravity and is a family of local HS theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between HS symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal HS fields (Fradkin–Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin–Felder–Shoikhet cocycle of Weyl algebra, which extends Segal’s action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle.

Weyl gravity extension of Higgs inflation

Weyl gravity extension of Higgs inflation

Analytical Approximations to Charged Black Hole Solutions in Einstein–Maxwell–Weyl Gravity

The homotopy analysis method (HAM) is a useful method to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl gravity coupled with Maxwell field and obtain analytical approximation solutions for charged black holes by using the HAM. It is found that the analytical approximate solutions are sufficiently accurate in the entire spacetime outside the black hole’s event horizon and also consistent with numerical ones for charged black holes in the Einstein–Maxwell–Weyl gravity.

Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitationallensing studies

Weyl's conformal gravity theory, which is considered as a compelling alternative to general relativity theory, has been claimed to describe the observed flat rotation curve feature of spiral galaxies without the need of invoking dark matter. However, it is important to examine whether the Weyl theory can also explain the relevant gravitational lensing observations correctly without considering any dark matter. In this regard, the gravitational bending angle in static spherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by several authors over the last two decades, but the results are found largely divergent. In this work, we have revisited the problem and obtain the correct and consistent expression of the deflection angle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We compare the prediction of Weyl gravity with the gravitational lensing observations of the rich galaxy clusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensing observations without considering dark matter.

Analysis of linearized Weyl gravity via the Hamilton–Jacobi method

The Hamilton–Jacobi formalism is used to analyze the Weyl theory in the weak-field limit. The complete set of involutive Hamiltonians is obtained, which are classified into involutive and non-involutive. The counting of degrees of freedom is performed. Additionally, the generalized brackets and gauge symmetries are reported.

Spontaneous scale symmetry breaking at high temperature

We consider a scale symmetric extension of the Standard Model Higgs scalar sector. The new sector, dilaton, is responsible for the generation of mass scales and may have geometric origin in the Weyl gravity {overset{sim }{R}}^2 term. We show how temperature as a mass scale breaks scale symmetry explicitly and through a nonvanishing thermal vev. In addition we demonstrate that cosmological evolution of the dilaton-Higgs system can lead to late time mass scales, which agree with the Standard Model.

Towards effective actions for the continuum limit of spin foams

Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to the continuum limit of spin foams are whether general relativity is reproduced and what type of corrections could emerge. As a central component for spin foam dynamics, recent results on the continuum limit of the Area Regge action suggest a close relation with actions for area metrics instead of a length metric. Inspired by these results, within the framework of modified Plebanski theory we construct a family of candidate actions for area metrics. These actions are expected to describe the continuum limit of spin foams and provide a starting point to explore phenomenological aspects of the large-scale dynamics of spin foams. More generally, they set the stage for exploring consequences of an enlargement of the configuration space for gravity from length to area metrics. The actions we construct lead to an effective action for the length metric, describing a non-local and ghost-free version of Einstein–Weyl gravity.

Nöther currents, black hole entropy universality and CFT duality in conformal Weyl gravity

In this paper, we study black hole entropy universality within the conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in conformal Weyl gravity via both the Nöther current method and Wald’s entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case, we couple the conformal Weyl gravity field equations to a near horizon (linear) [Formula: see text] gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However, despite non-universality, the respective black hole entropies are in congruence with Wald’s entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call [Formula: see text] and relating to the Weyl anomaly coefficient. The construction follows an [Formula: see text] correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work.

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

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.

Cosmological particle creation in Weyl geometry

We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the Universe ‘from nothing’ in the vacuum state, we investigated the problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for dark matter.

Varying-G gravity: physical properties, asymptotic regimes, and Green’s functions, an event horizon, the vacuum energy density, and the external pressure that modifies Jeans stability

ABSTRACT We study varying-G gravity and we add the necessary proofs (general force law, asymptotic forms, and Green’s functions, vacuum and external pressures, linearization of perturbations leading to a new Jeans stability criterion, and a physical origin) to elevate this novel idea to the status of a classical theory. The theory we lay out is not merely a correction to Newtonian gravity, it is a brand-new theory of gravity that encompasses the Newtonian framework and weak-field Weyl gravity in the limit of high accelerations, as well as Modified Newtonian Dynamics (MOND) in the opposite limit. In varying-G gravity, the source of the potential of a spherical mass distribution M(x) is σ(dG/dx) + (G/x2)(dM/dx), where x is the dimensionless radial coordinate and σ(x) = M(x)/x2 is the surface density away from the center x = 0. We calculate the potential $\Phi (x)=\int {G(x)\, \sigma (x)\, dx}$ from Poisson’s equation and the radial acceleration $a(x) = G(x)\, \sigma (x)$. Furthermore, a non-linear scaling transformation of the radial coordinate $x\in (0, \infty)\longmapsto \xi \in (0, 1)$ with scale factor ξ/x ∝ 1/G produces a finite space, in which the spherical surface ξ = 1 is an event horizon. In this classical context, it is the coupling of σ(x) to the gradient dG/dx in the above source that modifies the dynamics at all astrophysical scales, including empty space (where dG/dx ≠ 0). In vacuum, the source σ(dG/dx) supports an energy density distribution that supplies a repelling pressure gradient outside of discrete isolated massive systems. Surprisingly, the same source becomes attractive in linearized perturbations, and its linear pressure gradient opposes the kinetic terms in the Jeans stability criterion.

Generalized Gibbons-Werner method for deflection angle

The Gibbons-Werner method has been widely used in the gravitational deflection problem of particles moving in the curved spacetime. By applying the Gauss-Bonnet theorem (GBT) to regions constructed in a two-dimensional manifold, the deflection angle can be expressed and calculated in a geometric manner. For asymptotically flat spacetimes, an infinite region is usually chosen. While for some asymptotically nonflat spacetimes, the infinite region is ill defined due to the singular behavior of the metric, thus some special regions were constructed to solve the ill-defined problem. We propose a generalized method in which the choice freedom of the region where the GBT is applied is significantly enlarged. Our generalized method not only describes the conventional methods uniformly, but also lead to a formula which greatly simplifies the calculation. Additionally, we work out the deflection angle of the massive particle in the static spherically symmetric spacetime in conformal Weyl gravity based on the generalized method and the new formula.