Suppose that we are in the Weak Field Condition, that is: $$g_{\mu\nu}=\eta _{\mu\nu}+h_{\mu\nu}$$ where $\eta _{\mu\nu}$ is the metric tensor of flat space time (Minkowski spacetime) and $h_{\mu\nu}$ is a perturbation such that: $$|h_{\mu\nu}|<<1$$ Perfect. But now I would like to find the tensor $g^{\mu\nu}$; by definition (it is by definition of $g^{\mu\nu}$, right?) we have: $$g_{\mu\lambda}g^{\lambda \nu}=\delta ^\nu _\mu$$ I am fine with all the above, but now it is said that from the previous equation we can derive that: $$g^{\mu\nu}=\eta^{\mu\nu}-h^{\mu\nu}$$ why? Can you show me the process behind this result?
Asked
Active
Viewed 218 times
