- #1
TerryW
Gold Member
- 191
- 13
Homework Statement
I've been working on Exercise 14.3 in MTW. This starts with the FLRW metric (see attachment) and asks that you find the connection coefficients and then produce the non-zero elements of the Riemann Tensor.
The answer given is that there are only 2 non-zero elements vis Rtχtχ and RχθχΘ.
My problem is that I have ended up with four additional non-zero components - RtΘtΘ, Rtφtφ, Rχφχφ andRΘφΘφ
The attachment lists the connection coefficients I've produced, a) by using the suggested methodology in the exercise (derive them from the geodesic equations) and to check my result by b) using the standard process of
Γμαβ= ½{gμα,β + gμβ,α - gαβ,μ}
I found an alternative version of the FLRW metric at the url given at the bottom of the attachment and used the connection coefficients derived in that example to produce the Riemann Tensor components and find that I get the same 6 non-zero components.
Two of the four unwanted components contain [itex]\ddot a[/itex] which come from the derivative wrt t of one of the connection coefficients. Clearly this element will not be eliminated by subtracting the product of two connection coefficients, neither of which contain [itex]\ddot a[/itex] .Can anyone suggest where I might be going wrong?
TerryW
Homework Equations
See attachment
The Attempt at a Solution
See attachment
[/B]