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Excersise [14.30]
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Joined: 04 Feb 2009, 15:52
Posts: 8
Excersise [14.30]
Regards to all you!

I´m not sure if the formula about the quantity of independents components of Riemann tensor is right. I think this value must be

I say this because:

(1)
Moreover and and then, there are components whose value is 0.

The second antisymmetry tells us that
So, there are components whose vale is 0, but the components were already counted in (1); and and . Then there are more null components.

So, R has not-null components (that is, independent components)

But the first antisymmetry tells us that half the components of R are dependent of another half, so the independent componets are

And the second antisymmetry tells us the same, so remain elements. The interchange symmetry tells the same, so remain elements.

The Bianchi symmetry implies that each component depends of another two elements, so only 2/3 of remaining indepependent components are really independent.

Then, finally, there are independent components in Riemann tensor R.

This is my reasoning. Is there misprint in the book? Am I right or I'm wrong? Please I wish someone answer me.
See you soon!!

07 Jun 2009, 09:07

Joined: 05 Jan 2009, 15:24
Posts: 4
Re: Excersise [14.30]
Hi there, don't have time to check through your derivation carefully, but your expression is certainly wrong, and Penroses is correct.

See for instance http://mathworld.wolfram.com/RiemannTensor.html.

Might have a look at it a bit later.

Sebastian

09 Jun 2009, 09:53
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