Question about transveresetraceless gauge in gravityby Neitrino Tags: gauge, gravity, transveresetraceless 

#1
Nov2312, 12:07 PM

P: 133

I have a question about gauges in gravity.
Symmetric tensor field in four dimensions has 10 independet components, when we want to describe massless spintwo 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 transversetraceless 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 



#2
Nov2312, 04:24 PM

Sci Advisor
Thanks
P: 3,851

Neitrino, As you say, the first step is to impose the harmonic gauge condition, h_{μν,}^{ν} = 0, or equivalently in momentum space, h_{μν}k^{ν} = 0. This can be done covariantly, and reduces the number of independent components from 10 to 6.
There remains the freedom of further gauge transformations, h_{μν} → h_{μν} + e_{(μ}k_{ν)}. These can be used to reduce the number of components from 6 to 2, but not in a Lorentz covariant manner. Choosing a rest frame, one can show it is possible to set h_{i0} = 0 and h_{ij} = 0. Then we also have h_{ij}k^{j} = 0. This is what we mean by transverse and traceless, namely transverse to the 3dimensional kvector. 



#3
Nov2412, 04:21 AM

P: 133

Thanks Bill_K for you help...
So is it (TT gauge) much the same as Coulomb gauge in vector field theory ? Thanks 


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