Solve Physics Q1 from 2007 Paper61. Cambridge Maths Postgrad

[dextercioby]

The separation is not fully done (there's some explicit and some implicit dependence of the Ricci tensor of u), however the second equation will lead you to a successful use of 1. and 2. in what I wrote above.

So post your final equation.

 

[latentcorpse]

The separation is not fully done (there's some explicit and some implicit dependence of the Ricci tensor of u), however the second equation will lead you to a successful use of 1. and 2. in what I wrote above.

So post your final equation.

Well, I don't knkow how to use that in 1.

However, for 2. I get:

k_aR^a{}_{[b}k_{c]}=0
\Rightarrow 4 \pi ( \rho + p) k_a u^a ( u_b k_c - u_c k_b) + ( 4 \pi p + \frac{1}{4} R)(k_bk_c-k_ck_b)=0

I'm getting pretty confused as to where this is going though!

 

[dextercioby]

What can you derive of what you've written ? The second term of the sum vanishes, right ? So ?

 

[latentcorpse]

What can you derive of what you've written ? The second term of the sum vanishes, right ? So ?

u_b k_c=u_ck_b?

Is it then just a case of contracting with k^c since that gives

u_b k_c k^c=u_c k^c k_b \Rightarrow u_b = \lambda k_b since k_ck^c, u_c k^c are both scalars, right?

 

[dextercioby]

Yes, finally. :)

Did you solve the rest of the exercises, in case you needed it ?