# Derivation of the wave equation on a curved space-time

#### Woolyabyss

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.

#### Attachments

• 20.3 KB Views: 35
Related Advanced Physics Homework News on Phys.org

#### Orodruin

Staff Emeritus
Science Advisor
Homework Helper
Gold Member
2018 Award
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 and dextercioby

#### 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. ;)

### Want to reply to this thread?

"Derivation of the wave equation on a curved space-time"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving