# Ricci Tensor of FRW

by psimeson
Tags: ricci, tensor
P: 19
 Quote by clamtrox No, you sum over ALL the indices!
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 seeing how we get $\dot{a}$2
P: 937
 Quote by psimeson 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 seeing how we get $\dot{a}$2
no no no, Ricci tensor is the trace of Riemann tensor, so $R^{\mu}_{r\mu r} = R^{t}_{rtr} +R^{r}_{rrr} + R^{\theta}_{r \theta r} + R^{\phi}_{r \phi r}$
P: 19
 Quote by clamtrox no no no, Ricci tensor is the trace of Riemann tensor, so $R^{\mu}_{r\mu r} = R^{t}_{rtr} +R^{r}_{rrr} + R^{\theta}_{r \theta r} + R^{\phi}_{r \phi r}$
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
 P: 19 I think I got it.. Thanks a lot

 Related Discussions Advanced Physics Homework 4 Differential Geometry 4 Special & General Relativity 28 Differential Geometry 0 Special & General Relativity 5