Recent content by tommyj

okay a sort of different approach but how about this. I'll start by the motivation with the light cone for 3D Minkowski (in polar coordinates). The light cone has normal n^a = (\frac{\partial}{\partial t} + \frac{\partial}{\partial r} )^a . We know that the integral curves of n^a are null...

Yes I did that example just now, I must apologize to robphy I thought he was just giving an example of a null hypersurface. Indeed, doing it for the Minkowski light cone things follow through as I had hoped (in this case it was clear that the spacelike surface would be 2 spheres, but it was good...

Using notation as George above, the basis for T_pN would be (n, e_2, e_3 ) .The two spacelike vectors would be e_2 , e_3 , not e_1 since this is not orthogonal to n . Hence, at this particular point p where we have this ortho basis, I would like to have T_pS = sp(e_2, e_3) for the...

Hi Why is it possible to be able to pick a spacelike 2 surface S that lies in a null hypersurface N? We know that all the tangents vectors to N are either spacelike or parrelel to the normal vector. I imagine we want to build up S as the surface that is tangent to all the spacelike vectors in...

Holy ish. I was just writing the thing out on here as I was still stuck, and I was just expanding things to make sure i copied it down correctyl when i realized I mixed up some letters. I see now that when you expand out all the others terms with the h's they all go to zero. Friday morning...

Hey WNB sorry to bring up an old thread but above you said 2h^{e}{}{}_{a}h^{f}{}{}_{b}h^{g}{}{}_{c}\nabla_{[e}\nabla_{f]}n_{g} \\ = D_{a}K_{bc} - D_{b}K_{ac} - h^{e}{}{}_{a}h^{f}{}{}_{b}h^{g}{}{}_{c}n^{d}\nabla_{d}n_{g}\nabla_{e}n_{f} +...

ah man I even noted the hypersurface orthogonal relation as I knew it would be useful but I forgot about it. You live and learn as they say. thanks a lot, I know how much effort it is to write tensor equations on here so I really appreciate it! I cannot see how to do the second part. Its...

Sorry to get your hopes up but I made mistakes in both parts! How did you do part a) may i ask? I can't get terms to disappear. Also, for part b) both constraints only seem to imply that F^{ab}\nabla _an_b=0 which don't really seem to help to solve for the time derivative of the initial...

EDIT dw i figured it out, not sure how to remove it though!

This question has been asked two years ago, but it wasn't resolved (I think). Here goes This problem is Problem 5 in Chapter 4. It is that T_{ab} is a symmetric, conserved field (T_{ab}=T_{ba}, \partial ^aT_{ab}=0) in Minkowski spacetime. Show that there is a tensor field U_{acbd} with the...

Then, to get the final result, we just use this fact \partial^cW_{c[ab]}=0 or \partial_c{W^c}_{\mu\nu}=0. Pretty sure what you said above was wrong, \partial ^cW_{c[ab]}=0 does not imply that \partial d ^cW_{cab}=0. If it did it would mean then the stress energy tensor is zero from the step...

great, excellent thanks for that! very nice solutions. thanks for recommending that book btw, my maths was a bit rusty at first but now I'm getting back into the swing of things. Starting chapter 4 officially tomorrow, I had a brief read through it last night and it look wonderful, am excited!

Hi, sorry to bother you but I was wondering if you might help me with one of walds problems. I am pretty sure its not too hard, but I've been out of maths for a while and its making me feel very stupid. The question is question 3 on here...

just ordered the first one, sounds great, thanks!

Oh my days. Thats basic algebra, how have I done that. I guess working on a building site has taken more out of me than I thought. thanks for (apart from to all the people who read this thread) sparing my blushes!