Related papers: Mannheim's linear potential in conformal gravity
We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specializing to static fields with spherical symmetry, we obtain a second-order equation for one of the…
In their original study of conformal gravity, a candidate alternate gravitational theory, Mannheim and Kazanas showed that in any empty vacuum region exterior to a localized static spherically symmetric gravitational source, the geometry…
We study the weak-field limit of the conformal Weyl gravity suggested by Mannheim as an alternative to Einstein's General Relativity modeling both dark matter and dark energy. We solve the field equations of the theory in the weak-field…
We show that gravity field equations based on a tensor with rank greater than 2 have consistency problems in the sense that integration constants in the solutions, such as the parameter $m$ in the Schwarzschild metric, do not allow for an…
We study the weak-field limit of the static spherically symmetric solution of the locally conformally invariant theory advocated in the recent past by Mannheim and Kazanas as an alternative to Einstein's General Relativity. In contrast with…
An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the…
Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised…
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…
A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1+r)^2 and r will be replaced by r/(1+r), where r is the Schwarzschild radial coordinate.…
The field equations of Mannheim's theory of conformal gravity with dynamic mass generation are solved numerically in the interior and exterior regions of a model spherically symmetric sun with matched boundary conditions at the surface. The…
In a recent paper (MNRAS 458, 4122 (2016)) K. Horne examined the effect of a conformally coupled scalar field (referred to as Higgs field) on the Mannheim-Kazanas metric $g_{\mu\nu}$, i.e. the static spherically symmetric metric within the…
We show that Mannheim's conformal gravity program, whose potential has a term proportional to $1/r$ and another term proportional to $r$, does not reduce to Newtonian gravity at short distances, unless one assumes undesirable singularities…
A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters $\Theta^{\mu\nu}$. A deformed real…
The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the…
We study weak-field solutions having spherical symmetry in $f(T)$ gravity; to this end, we solve the field equations for a non diagonal tetrad, starting from Lagrangian in the form $f(T)=T+\alpha T^{n}$, where $\alpha$ is a small constant,…
A general analytic procedure is developed for the post-Newtonian limit of $f(R)$-gravity with metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method…
We present a Lorentz gauge theory of gravity in which the metric is not dynamical. Spherically symmetric weak field solutions are studied. We show that this solution contains the Schwarzschild spacetime at least to the first order of…
The equations of motion of four-dimensional conformal gravity, whose Lagrangian is the square of the Weyl tensor, require that the Bach tensor $E_{\mu\nu}= (\nabla^\rho\nabla^\sigma + \ft12 R^{\rho\sigma})C_{\mu\rho\nu\sigma}$ vanishes.…
General relativity postulates that the gravity field is defined on a Riemannian manifold. The field equations are $R^\mu_\nu = 0$ i.e. Ricci's curvature tensor vanishes. The field equations have to be augmented by natural physical…
We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general…