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Derivation of the wave equation on a curved space-time

Problem 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.
 

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Orodruin

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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.
 
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.
 
Out of curiosity - what level of Physics is this?
 
Physics?
I thought it was Greek. ;)
 

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