- #1
binbagsss
- 1,277
- 11
I have the expression ##g_{ab}=\eta_{ab}+\epsilon h_{ab}##,
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.
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.