I read about lovelock gravity:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Lovelock_theory_of_gravity

I dont undestand how generate a Riemman tensor [tex]R_{ijkl}[/tex] in the expression:

[tex]\delta^{abcd}_{ABCD}R^{AB}_{ab}R^{CD}_{cd} = R_{ijkl}R^{ijkl}-4R_{ij}R^{ij}+R^2[/tex]

`

[tex]\delta^{abcd}_{ABCD}[/tex] is the generalized kronecker delta,

i understan that a term

[tex]\delta^a_A \delta^b_B \delta^c_C \delta^d_D R^{AB}_{ab}R^{CD}_{cd} = R^2[/tex]

but , for example

[tex]\delta^a_A \delta^b_B \delta^c_D \delta^d_C R^{AB}_{ab}R^{CD}_{cd} ??[/tex]

for example , how i find the term [tex]R_{ijkl}[/tex] ?

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# Lovelock gravity

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