Recent content by gravity90

Thank you again for your response. But what is the difference between keeping u^a or u_a from a physical point of view?

I will use:\frac{1}{√-g} \frac{δ(√-g)}{δg^{μν}} = - 1/2 g_{μν} This is what I found in the Carroll's textbook and it seems right. But the thing is that the indices a,b are mute (g^{ab} u_a u_b) so upon variation with respect to δg^{cd} or δg_{cd} we should get the same result.

Thank you very much for your response. But why don't we use: \frac{δg^{ab}}{δg^{cd}} = {δ^a}_c {δ^b}_d or \frac{δg_{ab}}{δg_{cd}} = {δ^c}_a{δ^d}_b ?

Hi everyone! There is something that I would like to ask you. Suppose you have \frac{1}{\sqrt{-g}} \frac{\delta (\sqrt{-g} (g^{ab} u_a u_b + 1))}{\delta g^{cd}} The outcome of this would be ##u_{c}u_{d}## or ##-u_{c} u_{d}## ? I am really confused.