Conformal Gravity Theory Research Articles

Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation

We study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. We find, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. We present the solutions to this fourth order equation and find that we are able to recover all of the standard Newton-Euler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, we make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales far outside of fundamental sources, or on the very smallest ones within their interiors. Our study enables us to deduce that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary.

Open questions in classical gravity

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second-order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's law of gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted (but actually still open to question) assumptions which go into the formulation of the standard second-order Einstein theory in the first place. In particular, we show that while the familiar second-order Poisson gravitational equation (and accordingly its second-order covariant Einstein generalization) may be sufficient to yield Newton's law of gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth-order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved nonluminous or dark matter.

Linear Potentials and Galactic Rotation Curves

We derive a simple, closed form expression for the potential of a thin exponential disk of stars interacting through gravitational potentials of the form $V(r)=-\beta /r+\gamma r/2$, the potential associated with fundamental sources in the fourth order conformal invariant theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Using the model, we obtain a reasonable fit (flat to within $\pm3\%$) to the (prototypical) NGC3198 $HI$ rotation curve data without the need for any non-luminous or dark matter. Our study suggests that th observed flatness of rotation curves may only be an intermediate phenomenon, and an asymptotic one.

ON THE HIGHER-DERIVATIVE CONFORMAL GRAVITY

We consider the fourth-order conformal gravity theory. The quantization of the theory is presented in detail. We also calculate, using the heat kernel method, the one-loop divergence and conformal anomaly.

Vacuum structure in quantum gravity

The physical interpretation of the Eguchi-Hanson (EH) instanton solution is suggested. This solution describes the tunneling transition which connects vacua with opposite orientations. The diagonal vacuum states are symmetric and antisymmetric superpositions of states with a given orientation. The EH instantons lead to appearance of the induced Einstein term and of the large induced cosmological term in the effective action of the conformal gravity theory.

Local symmetries in extended conformal gravity and conformal supergravity in superspace

The extended conformal field theory of gravity is discussed, and its local symmetries are compared to those of Einstein and standard Weyl theories. It is then shown that the local symmetries of the extended conformal geometry are also natural for the construction of SU(N)-extended conformal supergravity theories in superspace. The natural superspace for the formulation of such theories is one with two sets of four-component fermionic variables which transform oppositely under scale transformations.

Geometrical transformation laws of fields in superunified theories

We present a systematic model-independent method of obtaining off-the-mass-shell transformation laws of fields in superunified theories. The method is applied to pure gravity, gravity coupled to Yang-Mills, conformal gravity, OSp( N;4) supergravity, and conformal supergravity theories.

Conformal and superconformal gravity and non-linear representations

Abstract The method of non-linear representations, when applied to the (super) conformal group, is shown not to be equivalent to the usual (super) conformal gravity theories. However, the requirement of invariance under the full (super) conformal group transformations, uniquely leads to the usual theories.