I have the expression ##g_{ab}=\eta_{ab}+\epsilon h_{ab}##,(adsbygoogle = window.adsbygoogle || []).push({});

The indices on ##h^{ab}## are raised with ##\eta^{ab}## to give ##g^{ab}=\eta^{ab}-\epsilon h^{ab}##

I am not seeing where the minus sign comes from.

So I know ##\eta^{ab}\eta_{bc}=\delta^{a}_{c}## and ##h^{ab}=\eta^{ac}\eta^{bd}h_{cd}## ,

And that ##\eta_{ab}## has signature ##(-,+,+,+)##,

Any help greatly appreciated.

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# Weak field approx raising index using minkowski metric

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