Conformal Gravity Rotation Curves with a Conformal Higgs Halo

Abstract

We discuss the effect of a conformally coupled Higgs field on conformal gravity (CG) predictions for the rotation curves of galaxies. The Mannheim-Kazanas (MK) metric is a valid vacuum solution of CG's 4-th order Poisson equation only if the Higgs field has a particular radial profile, S(r)=S_0 a/(r+a), decreasing from S_0 at r=0 with radial scale length a. Since particle rest masses scale with S(r)/S_0, their world lines do not follow time-like geodesics of the MK metric g_ab, as previously assumed, but rather those of the Higgs-frame MK metric Omega^2 g_ab, with the conformal factor Omega(r)=S(r)/S_0. We show that the required stretching of the MK metric exactly cancels the linear potential that has been invoked to fit galaxy rotation curves without dark matter. We also formulate, for spherical structures with a Higgs halo S(r), the CG equations that must be solved for viable astrophysical tests of CG using galaxy and cluster dynamics and lensing.

8 pages, 2 figures, MNRAS in press

References in corpus (5)

• Fourth order Weyl gravity
• Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields
• Light deflection in Weyl gravity: critical distances for photon paths
• On the Null Trajectories in Conformal Weyl Gravity
• Gravity coupled to a scalar field in extra dimensions

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• Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect
• Motion of massive particles around a charged Weyl black hole and the geodetic precession of orbiting gyroscopes
• Conformal gravity does not predict flat galaxy rotation curves
• Conformal gravity: light deflection revisited and the galactic rotation curve failure
• The covariant approach to static spacetimes in Einstein and extended gravity theories
• Conformally-rescaled Schwarzschild metrics do not predict flat galaxy rotation curves
• Gravitational waves from inspiralling compact binaries in conformal gravity
• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• Critique of the use of geodesics in astrophysics and cosmology
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Structure of conformal gravity in the presence of a scale breaking scalar field
• The Scalar Mode of Gravity