Weak gravity approximation gauge invariance

  • Thread starter Dixanadu
  • Start date
Hey guys,

So I have a question about the gauge invariance of the weak field approximation. So if I write the approximation as

[itex]\Box h^{\mu\nu} -\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha})+\partial^{\mu}\partial^{\nu}h=0[/itex]

then this is invariant under the gauge transformation

[itex]\delta h^{\mu\nu}=\partial^{\mu}\epsilon^{\nu}+\partial^{\nu}\epsilon^{\mu}+\mathcal{O}(\epsilon, h)[/itex]

if you ignore the correction terms. So my question is...how does this variation come about? I mean how would I calculate this variation from first principles, using [itex]g^{\mu\nu}(x)=\eta^{\mu\nu}+h^{\mu\nu}(x)[/itex]?

I looked at wikipedia and I didnt understand a word...so can someone please offer a simplified explanation of how to achieve this expression?

Thanks guys!
 

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

Hot Threads

Top