- #1
Neitrino
- 137
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I have a question about gauges in gravity.
Symmetric tensor field in four dimensions has 10 independet components, when we want to describe massless spin-two field (graviton) we impose harmonic gauge which reduces 10 independet components to 6 and afterwards we use diff invariance and eventually go down from 6 to 2 independet components. And all this happens with harmonic gauge.
++++++++++++++++++++++++++++++++++++++++
What is a transverse-traceless gauge?
Transverese means d_mu (h_mu_nu)=0 and this puts constraints on 4 components out of initial 10 components of symmetric tensor...
Traceless means Tr (h_mu_nu)=0 and this puts constraint on 1 component...
So TT gauge puts constraints 5 constraints on 10 components of symmetric tensor field... and what to do next how to reduce to 2 components to describe graviton ... how do i cast TT gauge in the same sense as i did for harmonic gauge above... ?
Thank you
Symmetric tensor field in four dimensions has 10 independet components, when we want to describe massless spin-two field (graviton) we impose harmonic gauge which reduces 10 independet components to 6 and afterwards we use diff invariance and eventually go down from 6 to 2 independet components. And all this happens with harmonic gauge.
++++++++++++++++++++++++++++++++++++++++
What is a transverse-traceless gauge?
Transverese means d_mu (h_mu_nu)=0 and this puts constraints on 4 components out of initial 10 components of symmetric tensor...
Traceless means Tr (h_mu_nu)=0 and this puts constraint on 1 component...
So TT gauge puts constraints 5 constraints on 10 components of symmetric tensor field... and what to do next how to reduce to 2 components to describe graviton ... how do i cast TT gauge in the same sense as i did for harmonic gauge above... ?
Thank you