Hi. Got 2 more questions on index placements.(adsbygoogle = window.adsbygoogle || []).push({});

1 - I found the following on an exam paper and it seems wrong to me. It concerns a weak perturbation to the Minkowski metric g_{ik}= η_{ik}+ h_{ik}. It then states that to first order in h_{ik}the contravariant metric tensor is g^{ik}= η^{ik}- η^{in}η^{km}h_{nk}. This seems wrong to me as the RHS has a free m index but the LHS does not. I think 2nd term on the RHS should be -η^{ai}η^{bk}h_{ab}which I think is equal to -h^{ik}. Am I right ?

2 - In some notes I found n_{uv}T^{uv}= T_{u}^{v}. This doesn't seem right either but i'm not sure exactly what it should be ? If I contract the u I get T_{v}^{v}but if I contract the v first I get T^{u}_{u}. Are these different ? Do they both equal scalar T ?

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# More index gymnastics question

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