Kavli Affiliate: Anthony Lasenby
| First 5 Authors: Michael Hobson, Anthony Lasenby, , ,
| Summary:
For conformally invariant gravity theories defined on Riemannian spacetime
and having the Schwarzschild–de-Sitter (SdS) metric as a solution in the
Einstein gauge, we consider whether one may conformally rescale this solution
to obtain flat rotation curves, such as those observed in galaxies, without the
need for dark matter. Contrary to recent claims in the literature, we show that
if one works in terms of quantities that can be physically measured, then in
any conformal frame the trajectories followed by `ordinary’ matter particles
are merely the timelike geodesics of the SdS metric, as one might expect. This
resolves the apparent frame dependence of physical predictions and
unambiguously yields rotation curves with no flat region. We also show that
attempts to model rising rotation curves by fitting the coefficient of the
quadratic term in the SdS metric individually for each galaxy are precluded,
since this coefficient is most naturally interpreted as proportional to a
global cosmological constant. We further extend our analysis beyond static,
spherically-symmetric systems to show that the invariance of particle dynamics
to the choice of conformal frame holds for arbitrary metrics, again as
expected. Moreover, we show that this conclusion remains valid for conformally
invariant gravity theories defined on more general Weyl–Cartan spacetimes,
which include Weyl, Riemann–Cartan and Riemannian spacetimes as special cases.
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