GW 017 linear Riemann Christoffel tensor gauge transform

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A gauge transform of the Riemann Christoffel curvature tensor with four downstairs indices leaves the components unchanged. I've made a sign error somewhere which I haven't quite got to the bottom of yet.
  1. Trin Tragula General Relativity
  2. general relativity
  3. gravitational waves
  4. Riemann curvature tensor
  5. linearized Riemann tensor
  6. Riemann Christoffel tensor
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Комментарии
Автор

Hi

I guess you lost a sign in somewhere. At 6:59 you cancel two terms, but they have the same sign.

Thanks for the step by step procedure, it save a lot of time.

uendertandrade
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Sir as long as I know in your form of the curvature tensor the h(mu alpha) term and the h(beta mu) term will have opposite signs infront of them and then it is a complete cancellation

sohamsen
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hi can you please give more clarity about where the error is ( both the terms having same signs )

cheriyanhomey
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I believe the sign errors originate from your Riemann curvature tensor, the third term should be negative and the fourth term should be positive.

sheikhpingu
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Please there are sign problem in the 4th line 2nd term and the cancellation is not valid as well

sohamsen