Gauge natural formulation of conformal gravity

2015

Annals of Physics

Self Cite

We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group.

Section: Notation and Naturalitymentioning

confidence: 99%

Section: Notation and Naturalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generally covariant vs. gauge structure for conformal field theories

2015

Annals of Physics

Self Cite

“…In [1] and [2] we discussed superpotentials for the so-called conformal gravity; see also [3]. There we found the expression for superpotential of the theory described by the Lagrangian…”

Section: Introductionmentioning

confidence: 97%

Conformal gravity as a Gauge natural theory

Int. J. Geom. Methods Mod. Phys.

2016

“…We emphasize that here these conformal transformations act on the metric field, leaving the position x on spacetime unaffected. The conformal invariance provides a traceless stress-energy tensor and a vanishing Noether current associated to it, showing that conformal transformations are pure gauge and thus non-dynamical [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Conformal gravity: light deflection revisited and the galactic rotation curve failure

Diaferio

2019

Class. Quantum Grav.

We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter γ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on γ. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on γ, i.e. by setting γ = 0, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters β and k of the Schwarzschild-like metric.