I just noticed that Cooperstock and Tieu have posted (last Friday) on arxiv a reponse (which I haven't actually read) to the criticisms leveled against their proposed solution to the problem of dark matter. Any comments? Regards, George
If I'm following what C&T are doing, they are creating an orthonormal basis of one-forms > [r/sqrt(r^2-N(r,z)^2),0,0,0]; > [0,exp(-v(r,z)/2),0,0]; > [0,0,exp(-v(r,z)/2),0,0]; > [ N(r,z)/sqrt( r^2-N(r,z)^2 ) ,0,0,sqrt(r^2-N(r,z)^2)]; which can be plugged directly into GRtII to give their metric. They are then finding the einstein tensor G in terms of the orthonormal basis, and equating all the pressure terms to zero. This gives me the first two of their equations in (6). But I can't quite figure out how they are getting the third. This is sort of a moot point, because I don't think C&T have really thought about the issue of the Komar mass being non-zero for a very short cylinder at z=0. C&T seem to actually admit that this happens, but don't seem to recognize properly the physical significance of this result.
The debate continues! Comments on "Perspectives on Galactic Dynamics via General Relativity" by Vogt & Letelier. Garth
Another approach by Cooperstock & Lieu in today's ArXiv: General relativistic velocity: the alternative to dark matter. They note: That reference [3] was to: Significant reduction of galactic dark matter by general relativity by Daniel Grumiller & H. Balasin, they say: . Any thoughts, is DM to explain galactic rotation curves really not required? Garth
I found the original C&T proposal very interesting but at the time was not sufficiently versed in GR to make a genuine appraisal of the validity in light of the criticism it received. I think this latest work is clever from both a purely scientific view as well as a more sociological one. They really aren't doing all that much new maths, but rather thinking about the observer dependent nature of an existing solution (collapsing spherical dust cloud) from none other than the most sacred of physics tomes, Landau and Lif****z (EDIT: PF won't let me write Lif$hitz, it thinks I'm trying to swear). There can be no argument this time about the validity of the solution, no one would dare publicly criticise L&L! Of course by their own admission, the collapsing dust cloud is not a reasonable physical analog of a cluster or galaxy, so this latest paper doesn't conclusively argue against DM in these systems, however they have (as long as there analysis is correct) shown that the central idea of the original proposal is somewhat vindicated. The idea (as I understand it) is that while the weak field limit of GR very closely matches the Newtonian result for a single point mass, the non-linear effects of GR (which means the fact that the effect of a sum of particles is not simply the sum of their individual potentials) are still important in the weak-field regime. The collapsing dust cloud example they go through is such a 'weak field' system and they demonstrate the significant departure of the GR result from the Newtonian result. This paves the way for, as they suggest, a true 'General Relativistic Virial Thereom' that would allow the true GR calculation for the expected velocity dispersion of a virialised object (such as a galaxy or cluster) for an object of a given mass. I haven't gone through the analysis in the paper in great detail yet, but at first glance it seems reasonable. I'm sure we haven't heard the last of this either way!