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 if and 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 µν , as previously assumed, but rather those of the Higgs-frame MK metricg µν = Ω 2 g µν , with the conformal factor Ω(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.

Profile of the \(^{12}\)CO(3-2) Emission Line Detected From the Debris Disc of 49 Ceti

“…Horne & Marsh [9] and later Beckwith & Sargent [10] have underlined the importance of the velocity gradient on the shape of the global Doppler velocity profile. The point is that different Doppler velocity intervals correspond to regions of the disc having very different areas: for a disc seen edge-on, both the smaller and larger Doppler velocities are found near x=0 and correspond to small areas while large |x| values relate to Doppler velocities close to the rotation velocity at the outer edge of the disc and correspond to large areas.…”

Gauge Choice in Conformal Gravity

“…In his paper, Horne (2016) examined the effect of the conformally coupled scalar field S(r) in (15) on the rotational curves of galaxies. In particular he showed that when the MK-metric written in the form (14) is stretched to what he calls the "Higgs frame", which is given by…”

“…In further discussion in his paper, Horne (2016) argues in favor of the metric in the Higgs conformal gauge vis-á-vis gravitational lensing. It has been noted that the γr term in the MK metric produces a negative angle light bending, i.e.…”

“…The cosmological constant Λ (which is equivalent to k) in the Schwarzschild de-Sitter geometry produces (Rindler & Ishak 2007) a negative contribution to the bending angle. But even if one questions the validity of the cosmological nature of the parameter γ, one can still make the theory attractive to null geodesics through an appropriate choice of the conformal gauge (Edery, Mèthot & Paranjape 2001) without the need to take γ < 0 as stated in Horne (2016), and so one can still do gravitational lensing in the MK-frame. Hence one can start with the metric in (7) and apply the conformal rescaling ds 2 →Ωds 2 followed by the coordinate transformation…”

Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

“…This final solution satisfies the vacuum field equations of the 4th order conformal Weyl gravity (CWG). The theory was therefore proposed as an alternative to the dark matter/dark energy scenario [9], and it has been studied from several points of view [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. May or may not being the proper alternative theory to Einstein gravity, the Weyl gravity however exhibits interesting properties.…”