Conformal Gravity Theory Research Articles

Wave metrics in the Cotton and conformal Killing gravity theories

Wave metrics in the Cotton and conformal Killing gravity theories

The κ-Model under the Test of the SPARC Database

Our main goal here is to conduct a comparative analysis between the well-known MOND theory and a more recent model called the κ-model. An additional connection, between the κ-model and two other novel MOND-type theories, Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, a0, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and κ-model) and/or to the dimension of the object under consideration (NFDG and κ-model). We then confer to parameter a0 a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the κ-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The κ-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now, we test this model on a large sample of galaxies issued from the SPARC database.

Observational redshift from general spherically symmetric black holes

In this work, we obtain an expression for the total observational frequency shift of photons emitted by massive geodesic particles circularly orbiting a black hole in a general spherically symmetric background. Our general relations are presented in terms of the metric components and their derivatives that characterize the black hole parameters. As a concrete example of this general relativistic approach, a special case is studied by applying the formalism to a nonsingular black hole conformally related to the Schwarzchild solution that possesses a length scale parameter l and an integer parameter N in addition to the black hole mass. Besides, we express the nonsingular black hole mass in terms of the observational redshift/blueshift. Finally, we investigate the effects of the free parameters of the conformal gravity theory on the observational frequency shift and compare results with those of the standard Schwarzschild black hole.

Images of nonsingular nonrotating black holes in conformal gravity

The accretion disk around a black hole and its emissions play an essential role in theoretical analysis of the black hole image. In the literature, two analytical toy models of accretions are widely adopted: the spherical model and the thin disk model. They are different geometrically but both thin optically. We polish them for free-falling accretions around static spherical black holes. As an application, we investigate the images of a class of nonsingular black holes conformally related to the Schwarzschild black hole. These black holes are vacuum solutions of a family of conformal gravity theories. Results are compared with the Schwarzschild black hole of the same mass. Our results indicate that the conformal factor does not affect the shadow radius seen by distant observers, but it leaves an imprint on the intensity image of black hole.

Conformal Renormalization of topological black holes in AdS6

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS6 theory.

Large scale structure formation for conformal theory of gravity

Large scale structure formation for conformal theory of 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.

Imprint of galactic rotation curves and metric fluctuations on the recombination era anisotropy

In applications of the conformal gravity theory it has been shown that a scale of order 105 Mpc due to large scale inhomogeneities such as clusters of galaxies is imprinted on the rotation curves of galaxies. Here we show that this same scale is imprinted on recombination era anisotropies in the cosmic microwave background. We revisit an analysis due to Mannheim and Horne, to show that in the conformal gravity theory the particle horizon distance scale of metric signals that originate in the primordial nucleosynthesis era at 109∘ K can encompass the entire recombination era sky. Similarly, the particle horizon distance scale of acoustic signals that originate at 1013∘ K can also encompass the entire recombination era sky. We show that the amplitudes of metric fluctuations that originate in the nucleosynthesis era can grow by a factor of 1012 by recombination, and by a factor of 1018 by the current time. In addition we find that without any period of exponential expansion a fluctuation amplitude that begins at a temperature of order 1033∘ K can grow by a factor of 1060 by recombination and by a factor of 1066 by the current time.

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.

Gravity, duality and conformal symmetry

The ( 4 , 0 ) supermultiplet in six dimensions contains a fourth-rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32 + 32 supersymmetries. Dimensional reduction on a circle gives the five dimensions N = 8 supergravity multiplet, with the fourth-rank tensor reducing to the graviton. If there is an interacting ( 4 , 0 ) theory, it should reduce to the full N = 8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual two-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacting ( 4 , 0 ) superconformal theory arises from a strong coupling limit of five-dimensional supergravity (suitably embedded in M -theory) describing M -theory at energies beyond the Planck scale. A key test for this is identified: M -theory toroidally compactified to five dimensions should have certain BPS states carrying a singlet central charge. These 1/2 BPS states are not related to any of the standard BPS states by dualities and do not correspond to non-singular soliton solutions—they appear to correspond to singular solutions related to gravitational instantons. Such states are needed to provide the Kaluza–Klein modes for the compactified six-dimensional theory. If there are no such states, then the conjecture is false, while the presence of such states would be strong indication that the conjecture could be true.

Gravity beyond Einstein? Yes, but in which direction?

We present qualitative arguments in favour of an extension of the theory of the gravitational interaction beyond that resulting from the Hilbert–Einstein action. To this end, we consider a locally conformal invariant theory of gravity, discussed some 30 years ago by Mannheim and Kazanas. We discuss its exact solution of the static, spherically symmetric configurations and, based on these, we revisit some of the outstanding problems associated with gravity, high energy interactions and sketch potential resolutions within the conformal gravity framework.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

Conformal Carrollian spin-3 gravity in 3D

We consider ultra-relativistic limit of the spin-2 and spin-3 conformal gravity theories in three dimensions, which leads to conformal Carrollian spin-2 gravity and its spin-3 analog. We also comment on the generalization of the result to arbitrary spin. The holographic examples show generalization in comparison with non-conformal Carrollian gravity.

Modified Newtonian Dynamics (MOND) vs Newtonian Dynamics: The Simple Test to Solve the Constant Speed of Galaxy Rotation

The rotation curve of galaxies for M33 in 1959 by Louise Volders gave the new hypothetical about the invisible matter that contributes inside of the galaxy, which later we call dark matter (DM). However, recently the theory about DM is still incomplete to understand this matter. This situation makes some scientists look for alternative ways such as f(R) gravity and conformal gravity theory. We have studied Modified Newtonian Dynamics (MOND) and Newtonian Dynamics (ND). We try to show the simple model that aims to give an analysis that MOND can correct to solve the constant speed of galaxy rotation. For simplicity, we consider the value of α = 1. The graph shows that the MOND model has a constant speed of 100 kilometres per second. While for the ND model, the speed will decrease for radius goes to infinity because the speed is dependent on r. Based on this result, we obtain that MOND can show the constant speed of galaxy rotation than ND. This result can conclude that MOND can solve the rotation curve of the galaxy.

Noether-Wald charges in six-dimensional Critical Gravity

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

Exact solution to perturbative conformal cosmology from recombination until the current era

In a previous paper (P. D. Mannheim, Phys. Rev. D 102, 123535 (2020)) we studied cosmological perturbation theory in the cosmology associated with the fourth-order derivative conformal gravity theory, and provided an exact solution to the theory in the recombination era. In this paper we present an exact solution that holds all the way from recombination until the current era.

Systematic study of background cosmology in unitary Poincaré gauge theories with application to emergent dark radiation and H0 tension

We propose a one-parameter extension to $\Lambda$CDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early universe redshifts away as hot dark matter, then quintessence, tracking the dominant equation-of-state parameter and leaving a falsifiable torsion field in the current epoch. This picture results from a new Poincar\'{e} gauge theory (PGT), one of the most promising among the latest batch of 58 PGTs found to be both power-counting renormalisable and free from ghosts and tachyons. We systematically categorise the cosmologies of 33 of these PGTs, as special cases of the most general parity-preserving, Ostrogradsky-stable PGT with a purely Yang-Mills action. The theory we consider contains two propagating massless gravitons, which may be $J^P=2^+$ (long-range gravitation and gravitational waves). A conspiracy among the coupling constants eliminates the spatial curvature $k\in\{\pm 1,0\}$ from the field equations. We show that this `$k$-screening' is not restricted to conformal gravity theories. The flat Friedmann equations are then emergent, with potentially tension-resolving freedom at the early scale-invariant epoch that reliably gives way to an attractor-like state of modern $\Lambda$CDM evolution. We compare with related theories and promising special cases, such as $k$-screened theories with negative-definite effective $k$, and more traditional theories with effective $\Lambda$ and a $J^P=0^-$ massive graviton (dark matter candidate). As a bonus, we analyse similarly constrained actions in the new extended Weyl gauge theory (eWGT). We show that in cosmology, PGT and eWGT span exactly the same classical phenomenology up to a linear map between their coupling constants, hinting at a deeper relationship between the two.

Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

In this paper, we apply the classical test of general relativity on a charged Weyl black hole, the exterior geometry of which is defined by altering the spherically symmetric solutions of the Weyl conformal theory of gravity. The tests are basically founded on scrutinizing the angular geodesics of light rays propagating in the gravitating system caused by the black hole. In this investigation, we bring detailed discussions about the bending of light, together with two other relativistic effects, known as the Shapiro and the Sagnac effects. We show that the results are in good conformity with the general relativistic effects, in addition to giving long-distance corrections caused by the cosmological nature of the background geometry under study.

Cosmological singularities in conformal Weyl gravity

In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis et al., and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that the conformal Weyl gravity can be free of the initial singularity problem. Then, following Barrow et al., we address the possible types of the finite-time future cosmological singularities. We discuss how these singularities also can be avoided in the context of this theory.

Effects of geometric optics in conformal Weyl gravity

We have investigated effect of geometric optics as the rotation of polarization vector of light in spacetime of gravitational compact object in the fourth-order theory of conformal Weyl gravity. The Pineault–Roeder method is applied to the rotating Weyl metric, and analytical results are obtained in the limit of weak field and or slow rotation. For the photon traveling parallel to the symmetry axes from the equatorial plane to infinity, the rotation of the polarization plane depends on the Weyl parameter gamma on the contrary to the Kerr spacetime where there is no rotation of polarization plane for this case.

Gravitational perturbations of nonsingular black holes in conformal gravity

It is believed that in the near future, gravitational wave detections will become a promising tool not only to test gravity theories, but also to probe extremely curved spacetime regions in our universe, such as the surroundings of black holes. In this paper, we investigate the quasinormal modes (QNMs) of the axial gravitational perturbations of a class of non-singular black holes conformally related to the Schwarzschild black hole. These non-singular black holes can be regarded as the vacuum solution of a family of conformal gravity theories which are invariant under conformal transformations. After conformal symmetry is broken, these black holes produce observational signatures different from those of the Schwarzschild black hole, such as their QNM frequencies. We assume that the spacetime is described by the Einstein equation with the effective energy momentum tensor of an anisotropic fluid. The master equation describing the QNMs is derived, and the QNM frequencies are evaluated with the Wentzel-Kramers-Brillouin (WKB) method up to the 6th order. As expected, the QNM spectra of these non-singular black holes deviate from those of the Schwarzschild black hole, indicating the possibility of testing these black hole solutions with the help of future gravitational wave detections.