pervect is correct again. I failed to use the chain rule and only differentiated the first derivative again, whilst the other part of the expression is also a function of r. This gives me he correct answer for all of my various starting cases. I knew it was an obvious error which lied...
I had a chance to recalulate my Ricci components in light of pervect's input, which I saw would change my sign, but ultimately I only got the negative of everything I originally had.
I am going to need a little more help. I will reference
"An exact solution" from Math Pages" at...
Thanks,
pervect is correct here. I lost the proper notation somewhere going back and forth between all the literature. Thanks for the MTW reference George. I bought mine when I was 13 years old as I thought it was neat and I might one day understand it. 31 years later that is starting to...
Schwarzschild Ricci components
Thanks for the responses. I have gone through every kind of starting point
Ansatz, et al, but come to the same point of one term in the end being off by a sign. I attached another Word document with an abbreviated version to better identify my problem...
I find the last two terms do cancel
y = x(Acos(4x) + Bsin(4x))
y' = Acos(4x) + Bsin(4x) + x (-4Asin(4x) + 4Bcos(4x))
y" = -4Asin(4x) + 4Bcos(4x) -4Asin(4x) + 4Bcos(4x) + x (-16Acos(4x) - 16Bsin(4x))
Putting back into the equation y" + 16y = 24cos(4x) gives
-4Asin(4x) + 4Bcos(4x)...
Attached is a word document where I am setting out the Ricci tensor components to solve for the terms in the line element equation and get to the Schwarzschild solution. I am overlooking something as I have a sign off in the Ricci components in comparison to the many texts and literature I have...