Conformal Weyl Gravity Research Articles

Conformal Weyl gravity and perihelion precession

We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim \& Kazanas (1989). To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant $\Lambda$. We show that besides the general relativistic terms obtained earlier from the Schwarzschild - de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the linear term $\gamma r$ in the metric. Using data for perihelion shift observations we obtain constraints on the value of the constant $\gamma$ similar to that obtained earlier using galactic rotational curves.

Modeling by autonomous Hamiltonian system: fixing the sign of a parameter

We illustrate how the application of autonomous Hamiltonian dynamical system can definitively fix a sign for an otherwise indefinite sign of a certain astrophysical parameter. To illustrate it, we shall consider the Mannheim–Kazanas-de Sitter solution of Weyl conformal gravity containing the parameter γ, which is believed to be significant in the galactic halo gravity. However, the sign of γ has so far been ambiguous. The strategy we adopt to fix it is to look for a finite maximum radius up to which the halo supports stable material circular orbits inside the de Sitter radius. The maximum radius for several observed lenses are calculated for both signs of γ, and with the observed value of cosmological constant Λ. These lenses (all having approximately the Einstein radius R E ≈ 1023 cm) consistently yield a maximum radius ( $$ R_{ \max }^{\text{stable}} \cong 4.25 \times 10^{27} {\text{cm}} $$ ) inside the de Sitter radius of the universe only when γ is negative, while a positive γ yields $$ R_{ \max }^{\text{stable}} $$ always exceeding the de Sitter radius.

Exact static cylindrical solution to conformal Weyl gravity

We present the exact exterior solution for a static and neutral cylindrically symmetric source in locally conformal invariant Weyl gravity. As a special case the general relativity analogue still can be attained, however only as a sub-family of solutions. Our solution contains a linear term that would thus result in a potential that grows linearly over large distances. This may have implications for exotic astrophysical structures as well as matter fields on the extremely small scale.

Light bending in the galactic halo by Rindler-Ishak method

After the work of Rindler and Ishak, it is now well established that thebending of light is influenced by the cosmological constant Λappearing in the Schwarzschild-de Sitter spacetime. We show that their method,when applied to the exact Mannheim-Kazanas-de Sitter solution of the Weylconformal gravity, nicely yields the expected answer together with severalother physically interesting new terms. Apart from Λ, the solution isparametrized by a conformal parameter γ, which is known to play adominant role in the galactic halo gravity. The application of the methodyields exactly the same γ− correction to Schwarzschild bending asobtained by standard methods. Different cases are analyzed, which include somecorrections to the special cases considered in the original paper by Rindlerand Ishak.

Bending of light in conformal Weyl gravity

We reexamine the bending of light issue associated with the metric of the static, spherically symmetric solution of Weyl gravity discovered by Mannheim and Kazanas (1989). To this end we employ the procedure used recently by Rindler and Ishak to obtain the bending angle of light by a centrally concentrated spherically symmetric matter distribution in a Schwarzschild-de Sitter background. In earlier studies the term {gamma}r in the metric led to the paradoxical result of a bending angle proportional to the photon impact parameter, when using the usual formalism appropriate to asymptotically flat space-times. However, employing the approach of light bending of Rindler and Ishak we show that the effects of this term are in fact insignificant, with the discrepancy between the two procedures attributed to the definition of the bending angle between the asymptotically flat and nonflat spaces.

General class of wormhole geometries in conformal Weyl gravity

In this work, a general class of wormhole geometries in conformal Weyl gravity is analyzed. A wide variety of exact solutions of asymptotically flat spacetimes is found, in which the stress–energy tensor profile differs radically from its general relativistic counterpart. In particular, a class of geometries is constructed that satisfies the energy conditions in the throat neighborhood, which is in clear contrast to the general relativistic solutions.

Q-plane-wave solutions of q-Weyl gravity

The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given.

Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-Abelian gauge fields, i.e. the Georgi–Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, providing a mechanism for supplying a scale in the theory. The vacuum solution corresponds to anti-de Sitter spacetime, while localized soliton solutions correspond to magnetic monopoles in asymptotically anti-de Sitter spacetime. This mechanism strengthens the reasons for considering conformally invariant matter-gravity theory, which has shown promising indications concerning the problem of missing matter in galactic rotation curves.

Q-conformal invariant equations and q-plane wave solutions

We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the study of quantum linear conformal (Weyl) gravity by writing the corresponding q-deformed equations.

Energy in generic higher curvature gravity theories

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with nontrivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and anti–de Sitter vacua are stable.

New vacuum solutions of conformal Weyl gravity

The Bach equation, i.e., the vacuum field equation following from the Lagrangian L=CijklCijkl, will be completely solved for the case that the metric is conformally related to the Cartesian product of two two-spaces; this covers the spherically and the plane symmetric space–times as special subcases. Contrary to other approaches, we make a covariant 2+2-decomposition of the field equation, and so we are able to apply results from two-dimensional gravity. Finally, some cosmological solutions will be presented and discussed.

Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity

Using Penrose diagrams the causal structure of the static spherically symmetric vacuum solution to conformal (Weyl) gravity is investigated. A striking aspect of the solution is an unexpected physical singularity at $r=0$ caused by a linear term in the metric. We explain how to calculate the deflection of light in coordinates where the metric is manifestly conformal to flat i.e. in coordinates where light moves in straight lines.

Topological black holes in Weyl conformal gravity

We present a class of exact solutions of Weyl conformal gravity, which have an interpretation as topological black holes. Solutions with negative, zero or positive scalar curvature at infinity are found, the former generalizing the well known topological black holes in anti-de Sitter gravity. The rather delicate question of thermodynamic properties of such objects in Weyl conformal gravity is discussed; suggesting that the thermodynamics of the solutions found should be treated within the framework of gravity as an induced phenomenon, in the spirit of Sakharov's work.

Matching Exterior to Interior Solutions in Weyl Gravity: Comment on ``Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves''

view Abstract Citations (14) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Matching Exterior to Interior Solutions in Weyl Gravity: Comment on ``Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves'' Perlick, Volker ; Xu, Chongming Abstract Recently Mannheim and Kazanas presented the static, spherically symmetric exact vacuum solution of Weyl gravity and suggested that it could be fitted to general relativistic experimental tests in the solar system and to the observed galactic rotation curves. Here we discuss matching this solution to an interior one that satisfies the weak energy condition and a regularity condition at the center. We show that this leads to contradiction of Mannheim & Kazanas's suggestion. Publication: The Astrophysical Journal Pub Date: August 1995 DOI: 10.1086/176030 Bibcode: 1995ApJ...449...47P Keywords: COSMOLOGY: THEORY; GRAVITATION; RELATIVITY full text sources ADS |

Can conformal Weyl gravity be considered a viable cosmological theory?

We present exact analytical solutions to the Conformal Weyl Gravity cosmological equations that are valid for both the matter and radiation dominated eras. The Primordial Nucleosynthesis process is also exhaustively studied. The main conclusion of our work is that cosmological models derived from this theory are not likely to reproduce the observational properties of our Universe. They fail to fulfill simultaneously the observational constraints on present cosmological parameters and on primordial light element abundances.

Conformal gravity and the flatness problem

The radiation and matter-dominated cosmologies associated with fourth-order conformal Weyl gravity, a theory which is currently being explored as a candidate alternative to the standard second-order Einstein theory, are presented. The theory naturally yields an open though nonetheless recollapsing universe which can even oscillate indefinitely, which appears to possess no flatness problem, which has a cosmology which could potentially be created out of nothing, which is singularity free, and which does not appear to require any cosmological dark matter.

Solutions to the Reissner-Nordström, Kerr, and Kerr-Newman problems in fourth-order conformal Weyl gravity.

We continue our study of the general structure of fourth-order conformal Weyl gravity which we are exploring as a possible theory of gravity, and in this paper we present three new exact solutions to the theory which we have found. First we present the complete and exact solution to the Reissner-Nordstr\"om problem associated with a static, spherically symmetric point electric and/or magnetic charge coupled to fourth-order conformal Weyl gravity. We find that, unlike the familiar second-order Einstein case where the modification to the Schwarzschild metric is in the form of a term which behaves like $\frac{1}{{r}^{2}}$, in the fourth-order case the modification is found to behave like $\frac{1}{r}$, i.e., just like the Newtonian potential term itself. Additionally, we present two further exact solutions to the theory which we have found, namely, those associated with the fourth-order Kerr and Kerr-Newman problems in which a stationary, axially symmetric rotating system with or without electric and/or magnetic charge is coupled to gravity.

The cosmological constant and the fate of the cosmon in Weyl conformal gravity

Abstract We discuss a generalization of the cosmon model by turning its global dilatation invariance into a local conformal invariance. In a Weyl realization of this symmetry, the “would-be” cosmon field is eaten up by a conformal gauge boson which acquires a large mass. The new model is used to relax the cosmological constant to zero by means of a probabilistic mechanism first suggested by Hawking in the framework of euclidean quantum gravity.

General structure of the gravitational equations of motion in conformal Weyl gravity

A general method for determining the structure of the gravitational equations of motion is presented in the fourth-order theory of gravity based on local conformal Weyl invariance of the gravitational action. The explicit structure for these equations is given for a time-dependent, spherically symmetric geometry.

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.