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

Abstract

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 $\gamma$ 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 $\gamma$. 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 $\gamma$, i.e. by setting $\gamma =0$, 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 $\beta$ and $k$ of the Schwarzschild-like metric.

arXiv comment16 pages, 1 figure. Revised version according to the referees comments. The results reported in the original version remain unchanged

References in corpus (41)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Planck 2015 results. XIII. Cosmological parameters
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Testing General Relativity with Present and Future Astrophysical Observations
• Binary Black Hole Mergers in the first Advanced LIGO Observing Run
• Alternatives to Dark Matter and Dark Energy
• Cosmological Tests of Gravity
• Making the Case for Conformal Gravity
• Small scale problems of the $\Lambda$CDM model: a short review
• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• Fitting galactic rotation curves with conformal gravity and a global quadratic potential
• Classical tests for Weyl gravity: deflection of light and time delay
• Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes
• Fake Conformal Symmetry in Conformal Cosmological Models
• Correct light deflection in Weyl conformal gravity
• Cosmological Perturbations in Conformal Gravity
• Gauge Formalism for General Relativity and Fermionic Matter
• Light deflection in Weyl gravity: constraints on the linear parameter
• Light deflection in Weyl gravity: critical distances for photon paths
• Gamma-ray bursts as cosmological probes: LambdaCDM vs. conformal gravity
• Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting
• Augmented Variational Principles and Relative Conservation Laws in Classical Field Theory
• Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
• Noether Charges, Brown-York Quasilocal Energy and Related Topics
• Can Conformal Weyl Gravity be Considered a Viable Cosmological Theory?
• Remarks on Noether charges and black holes entropy
• ADM Pseudotensors, Conserved Quantities and Covariant Conservation Laws in General Relativity
• On the Null Trajectories in Conformal Weyl Gravity
• X-ray clusters of galaxies in conformal gravity
• Inflationary cosmology from quantum Conformal Gravity
• Conformal Gravity Rotation Curves with a Conformal Higgs Halo
• The Entropy of Taub-Bolt Solution
• Spherical Skyrmion black holes as gravitational lenses
• Gauge Natural Formulation of Conformal Theory of Gravity
• A Noncompact Weyl-Einstein-Yang-Mills Model: A Semiclassical Quantum Gravity
• Is the Cosmological Constant Problem Properly Posed?
• The relative energy of homogeneous and isotropic universes from variational principles
• Conformal Gravity as a Gauge Natural Theory

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