There are a variety of general relativistic effects that could explain dark matter phenomena. There seems to be a very solid analysis, however, concluding that gravitomagnetic effects in linearised general relativity are not among them.
We investigate recent claims that gravitomagnetic effects in linearised general relativity can explain flat and rising rotation curves, such as those observed in galaxies, without the need for dark matter.
If one models a galaxy as an axisymmetric, stationary, rotating, non-relativistic and pressureless 'dust' of stars in the gravitoelectromagnetic (GEM) formalism, we show that GEM effects on the circular velocity v of a star are O(10^−6) smaller than the standard Newtonian (gravitoelectric) effects.
Moreover, we find that gravitomagnetic effects are O(10^−6) too small to provide the vertical support necessary to maintain the dynamical equilibrium assumed.
These issues are obscured if one constructs a single equation for v, as considered previously. We nevertheless solve this equation for a galaxy having a Miyamoto--Nagai density profile. We show that for the values of the mass, M, and semi-major and semi-minor axes, a and b, typical for a dwarf galaxy, the rotation curve depends only very weakly on M. Moreover, for aspect ratios a/b>2, the rotation curves are concave over their entire range, which does not match observations in any galaxy.
Most importantly, we show that for the poloidal gravitomagnetic flux ψ to provide the necessary vertical support, it must become singular at the origin. This originates from the unwitting, but forbidden, inclusion of free-space solutions of the Poisson-like equation that determines ψ, hence ruling out the methodology as a means of explaining flat galaxy rotation curves.
We further show that recent deliberate attempts to leverage such free-space solutions against the rotation curve problem yield no deterministic modification outside the thin disk approximation, and that, in any case, the homogeneous contributions to ψ are ruled out by the boundary value problem posed by any physical axisymmetric galaxy.
A. N. Lasenby, M. P. Hobson, W. E. V. Barker, "Gravitomagnetism and galaxy rotation curves: a cautionary tale" arXiv:2303.06115 (March 10, 2023).
3 comments:
Did you read this paper?
They comment on Deur. They confirm my suspicions. I would suggest you move on, perhaps to refracted gravity.
They do indeed, although only in the preface - citing one unpublished and non-preprinted manuscript in end note 26 (which I look forward to reading when it eventually comes out) and another paper purporting to refute a non-Deur paper by F.I. Cooperstock and S. Tieu making a different analysis (in end note 27). The paper taht end note 27 purports to refute and its abstract is:
"We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is 10^−21.75 kg⋅m^−3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed."
F.I. Cooperstock, S. Tieu, "Galactic dynamics via general relativity: a compilation and new developments." 22 Int. J. Mod. Phys. A 2293–2325 (2007). arXiv:astro-ph/0610370 See also follow up papers in 2007, in 2011, and 2015.
The main paper is about claims that GEM effects can explain DM, which have been refuted before.
This said, I have never been very concerned with whether Deur's GR-SI is indeed orthodox GR or is in fact a modification of GR. The important point is that it is a theory that explains all of the data in a minimalist manner that conserves matter-energy.
They do indeed, although only in the preface - citing one unpublished and non-preprinted manuscript in end note 26 (which I look forward to reading when it eventually comes out) a
they also state Deur's claims are completely unsupported by numerical general relativity, and that his paper is to do to GEM what previous GR experts did to Deur
This said, I have never been very concerned with whether Deur's GR-SI is indeed orthodox GR or is in fact a modification of GR. The important point is that it is a theory that explains all of the data in a minimalist manner that conserves matter-energy.
But it is wrong. Time to move on.
refracted gravity seems more promising and similar to Deur in spirit
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