Talk:Dust solution

Characteristic Polynomial

I changed the following text in the article:

The characteristic polynomial

$\chi (\lambda )=\lambda ^{4}+a_{3}\,\lambda ^{3}+a_{2}\,\lambda ^{2}+a_{1}\,\lambda +a_{0}$

of the Einstein tensor in a dust solution must have the form

$\chi (\lambda )=\left(\lambda -8\pi \mu \right)\,\lambda ^{3}$

Multiplying out this product, we find that the coefficients must satisfy the following three algebraically independent (and invariant) conditions:

$a_{2}\,=a_{3}=a_{4}=0$

to:

$a_{0}\,=a_{1}=a_{2}=0$

The expression of the characteristic polynomial doesn't include an a_4 term, indicating that something must be wrong. I made the following change assuming that the mistake was a trivial one, that the person who originally wrote the article accidentally mislabeled the coefficients of the polynomial in the second expression. (probably left to right, rather than right to left) If this is not the case and there was actually something non-obvious going on in the mathematics between the original expression of the characteristic polynomial and the expression of its solution, I'd appreciate it if whoever makes the correction also explains what is going on *and* puts a label for the a_4 term in the original polynomial.

Also: I'm not 100% sure if my change in labeling will have an effect upon the later statement of the powers of the traces via Newton's identities, although, I *think* that is okay. I'd appreciate a double check, if you have the technical expertise to do so. —Preceding unsigned comment added by 76.91.90.112 (talk) 22:04, 28 June 2008 (UTC)

"dust"

Shouldn't there be a physical justification for the naming?

The everyday notion of "dust" is a suspension of tiny solid particles (each consisting of very many atoms and therefore having many phonon modes which cause the particles to absorb radiation and look opaque). The common notion of a pressure difference is felt through the force of many elastic collisions of microscopic particles upon container walls (pressure being related to the variance in velocity between constituent particles). If the partial pressure of a "dust" were made high, the inter-collisions would tend to break the solid particles apart into a gas (a suspension of individual molecules, which do not retain the phonon modes and so look transparent to most colours of radiation), hence in astrophysics dust equates with vanishing pressure. Cesiumfrog (talk) 03:38, 17 June 2009 (UTC)

Dust (relativity)

I think this article should be renamed "Dust (relativity)", not "Dust solution". (Actually, both articles presently exist, so I am suggesting performing the merge in the opposite direction to what has already been proposed.) The main focus of the article is already the concept of dust in SR and GR, as exemplified by the current section on mathematical definition (which defines relativistic dust generally rather than defining dust solutions specifically - indeed the latter would concentrate primarily on the simplified form of the EFE). Its focus is not solely the "solutions" themselves (i.e., particular mathematical expressions for metric tensors in coordinate charts) and these are already relegated to only a subsection here. (Also, I think it would be very appropriate to include a brief subsection noting the experimental relevence, e.g., mentioning intergalactic dust clouds and interstellar dust clouds. Relativistic dust seems a far more generally useful physics article for wikipedia to cover, rather than the esoteric, theoretical, almost eccentric subtopic of exclusively these solutions for their own sake alone.) Cesiumfrog (talk) 02:54, 18 December 2010 (UTC)