The discussion revolves around the recent response by Cooperstock and Tieu to criticisms of their proposed solution to the dark matter problem in astrophysics. Participants explore various aspects of their model, including its mathematical formulation, implications for galactic dynamics, and the validity of the criticisms it has received.
Participants express a range of views, with some supporting the Cooperstock and Tieu model while others raise significant criticisms. There is no consensus on the validity of their approach or the criticisms it faces.
Participants highlight limitations in the current understanding of the model, including unresolved mathematical steps and the dependence on specific physical analogies that may not fully represent galactic dynamics.
Abstract
In this comment we question some arguments presented in http://arxiv.org/abs/astro-ph/0512048 to refuse the presence of an singular mass surface layer. In particular, incorrect expressions are used for the disk’s surface mass density. We also point out that the procedure of removing the descontinuity on the z = 0 plane with a region of continuous density gradient generates other two regions of descontinuities with singular mass surface layers making the model unrealistic.
The recently proposed Cooperstock-Tieu galaxy model claims to explain the flat rotation curves without dark matter. The purpose of this note is to show that this model is internally inconsistent and thus cannot be considered a valid solution. Moreover, by making the solution consistent the ability to explain the flat rotation curves is lost.
A more Machian alternative anybody?However, the flat rotation curves seem to imply a large inertial induction effect, where the rotating inner matter boosts the rotation of the outer matter, leveling off the rotation curve, which is what the Cooperstock-Tieu model attempts to describe within general relativity. Since their solution predicts a matter density well within visible limits it is quite possible that their solution represents an alternative, more Machian, gravitational theory where inertial induction effects are much larger than in General Relativity.
They note:We consider the gravitational collapse of a spherically symmetric ball of dust in the general relativistic weak gravity regime. The velocity of the matter as viewed by external observers is compared to the velocity gauged by local observers. While the comparison in the case of very strong gravity is seen to follow the pattern familiar from studies of test particles falling towards a concentrated mass, the case of weak gravity is very different. The velocity of the dust that is witnessed by external observers is derived for the critically open case and is seen to differ markedly from the expectations based upon Newtonian gravity theory. Viewed as an idealized model for a cluster of galaxies, we find that with the general relativistic velocity expression, the higher-than-expected constituent velocities observed can be readily correlated with the solely baryonic measure of the mass, obviating the need to introduce extraneous dark matter. Hitherto unexplained and subject-to-reinterpretation astrophysical phenomena could also be considered within this context. It is suggested that an attempt be made to formulate an experimental design at smaller scales simulating or realizing a collapse with the aim of implementing a new test of general relativity.
That reference [3] was to: Significant reduction of galactic dark matter by general relativity by Daniel Grumiller & H. Balasin, they say:Various critics have claimed that our results stemmed from a singular surface layer of mass but we have shown that the singularity actually represents the benign incorporation of a discontinuity in density gradient. As well, a different approach [3] largely supported our central thesis.
.Exact stationary axially symmetric solutions of the 4D Einstein equations with co-rotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments over-estimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down globally, even though it is valid locally everywhere.