Recent content by psimeson

I think I got it.. Thanks a lot

So that means, for x, y and z, I have: R^{\mu}_{x\mu x} = R^{t}_{xtx} +R^{x}_{xxx} + R^{y}_{x y x} + R^{z}_{xzx} right? But the second term is zero and 3rd and 4th term does not have time in it so I will not "a" contribution from them

i.e t= μ and t = \nu How the does Ricci tensor equation looks like then? R_{rr} = R^{\mu}_{r\mu r} + R^{\nu}_{r\nu r} Since R^{\mu}_{r\mu r} = a\ddot{a} and R^{\nu}_{r\nu r} = a\ddot{a} R_{rr} = 2 a\ddot{a} that's not correct. I don't know I am getting confused. I am not...

isn't it same as as R_{rr} = R^{t}_{r t r} I am confused here. I am talking about (74) i.e Rij from: http://www.phys.washington.edu/users/dbkaplan/555/lecture_04.pdf

if k = 0 then you get only a\ddot{a} But according to the notes, we should get a\ddot{a} + 2\dot{a}2

Here's my line element: ds2 = -dt2 + a2(t) (dx2 + dy2 + dz2) Can someone please show couple of steps here?

My formula is actually: R^t_{xtx}=\Gamma ^{t}_{xx,t}-\Gamma ^{t}_{xt,x}+\Gamma ^{n}_{xx}\Gamma ^{t}_{nt}-\Gamma ^{n}_{xt}\Gamma ^{t}_{nx}

Sorry that's a typo, it's "a\dot{a}" only

Yes, I used the above mentioned formula. where, r = q = t and m=s= x

I did by hand and the significant Christoffel symbols here are: \Gamma^{t}_{xx} = a\ddot{a} \Gamma^{x}_{tx} = \frac{\dot{a}}{a} I am following Sean's note too. I don't know when I try to calculate R_{xx} i.e. R^{t}_{xtx}. I am not getting the correct answer

I am trying to understand FRW universe. To do so I am following the link below: http://www.phys.washington.edu/users/dbkaplan/555/lecture_04.pdf I am confused at equation 74. I got R00 but for Rij part I am always getting a\ddot{a}. I am trying to solve it for k =0. Can some please...

I have my solution in the above post I am getting \frac{1}{(1+2ϕ)}ϕ,μ\dot{x}μ=0 I think my derivatives are correct

For time, Christoffel Symbol should be: {\Gamma^t}_{it} = x_i\frac{\phi'(r)}{r} But by doing the way you suggest I didn't get the answer: \frac{d}{d\tau} \frac{\partial L}{\partial \dot{t}} = -2\frac{d}{d\tau} [(1+2\phi) \dot{t}] = -2((1+2\phi)\ddot{t} + 2\dot{t} \phi_{,\mu}...

I didn't get how you get {\mu}...why are you using lower index \dot{x}_i \frac{d}{d\tau} \frac{\partial L}{\partial \dot{x}_i} = 2\frac{d}{d\tau} [(1+2\phi) \dot{x}_i] = 2((1+2\phi)\ddot{x}_i + 2\dot{x}_i \phi_{,\mu} \dot{x}^{\mu}) What is \dot{x}_j \dot{x}^j? \frac{\partial...

I know that phi is function of r and I am having hard time to differentiate it. I just got stuck. Since r = sqrt (x^2 + y^2+ z^2) . How can it depend on t. The way it can depend on t by using the definition of proper time. Sorry, I am just lost.