Recent content by zn5252

Yes there is a much shorter version using Lie derivatives indeed...

Ok let us expand out your expression above : [SIZE="3"] (pμξμ),λ\frac{∂(p_{v}η^{v})}{∂p_{λ}}−(pvηv),λ\frac{∂(p_{v}ε^{v})}{∂p_{λ}} = ( pμ,λεμ + pμεμ,λ ) ( ηλ + pv\frac{∂(η^{v})}{∂p_{λ}} ) - ( pv,ληv + pvηv,λ ) ( ελ + pv\frac{∂(ε^{v})}{∂p_{λ}} ) Now we have : \frac{∂(ε^{v})}{∂p_{λ}} = 0 =...

hey Mate, Thanks for your reply. Well it seems I got confused here. I had based my second commutation on the first one. In my very first attempt I had indeed written your expression but had forgotten that the other variable was x not either of the killing vectors ε or η... Damn that got me...

hi there, In this Ex ( see attached snapshot ), point b), the poisson bracket equation is not so straightforward to obtain. Please correct my Poisson Bracket expansion here : The first one which is provided is simpler : [ε,η] = εμδμηρ - ημδμερ = ζη and the monster one : [pε,pη] =...

Great . Thanks ! I have Wheeler and Ciufolini's "Gravitation and Inertia". I will check that out. Thanks for mentioning that.

Indeed I saw it and also attempted to derive my own which yielded the correct result based on the continuity equation and on the assumption that the divergence of the density is negligible...

You may also see the derivation in Dirac's book : General theory of Relativity under equation 11.1 if I'm not wrong

Indeed this is what part b) mentions. Thanks !

Oh I see Bill. I did not get to part b) yet .

hello In MTW exercise 22.6, given a fluid 4-velocity u, why the expression : ∇.u is called an expansion of the fluid world lines ? Is the following reasoning correct ? We know that the commutator : ∇BA - ∇AB is (see MTW box 9.2) is the failure of the quadrilateral formed by the vectors A...

This is related to the last question of MTW ex 21.21

All N = 2 spaces are conformally flat. This would mean that since the Weyl tensor vanishes for the conformal space whose Riemann tensor has the form [R], thus one can conclude that for N=2, the Weyl tensor is null. This might make sense. But i do not know why the computation above did not...

hello, The Weyl tensor is: http://ars.els-cdn.com/content/image/1-s2.0-S0550321305002828-si53.gif In 2 dimensions , the Riemann tensor is (see MTW ex 14.2): Rabcd = K( gacgbd - gadgbc ) [R] Now the Weyl tensor must vanish in 2 dimensions. However, working with the g g = [-1 0 0...