Derivation of the wave equation on a curved space-time

[Woolyabyss]

Homework Statement

Problem attached as image

Relevant Equations

$\nabla^a F_{ab} = 0$
$\nabla_a F_{bc} + \nabla_b F_{ca} + \nabla_c F_{ab} = 0$

I'm confused by this question, from minimal coupling shouldn't the answer simply be $\nabla^a \nabla_a F_{bc} = 0$? Any help would be appreciated.

EDIT: I should also point out $F_{ab}$ is the EM tensor.

 

[Orodruin]

You have not given the starting point and so the goal is unclear. Both expressions reduce to $\partial^\lambda\partial_\lambda F_{\mu\nu}=0$ in Minkowski coordinates on flat spacetime.

 

[Woolyabyss]

You have not given the starting point and so the goal is unclear. Both expressions reduce to $\partial^\lambda\partial_\lambda F_{\mu\nu}=0$ in Minkowski coordinates on flat spacetime.

Thanks for the reply, I managed to work out the answer my issue turned out to be I wasn't taking into account that covariant derivatives don't commute.

 

[Professor Hulk]

Out of curiosity - what level of Physics is this?

 

[Ralph Rotten]

Physics?
I thought it was Greek. ;)