I need to find the variation of the purely covariant Riemann tensor with respect to the metric gμν, i.e. δRρσμν.
I know that, Rρσμν=gρηRησμν
and δRησμν=∇μ(δΓηνσ)−∇ν(δΓημσ).
So do I need to use the product rule like so, δRρσμν=δ(gρηRησμν)=δ(gρη)Rησμν+gρηδ(Rησμν),
which gives me a relatively messy answer. Is there another way to approach this?
No comments:
Post a Comment