question

[alejandrito20]

in a spacetime with axial gauge fluctuation of metric component [math]h_{uv}[/math]

¿what mean the transverse traceless TT [math]h_{uv}^{TT}[/math], and non transverse traceless NT [math]h_{uv}^{NT}[/math] component??

[ajb]

You are thinking about gauge fixing using the axial gauge and then showing that the gravitational waves have two polarisations? (The de Donder gauge condition seems to be used more, then there is a related condition call the radiation gauge (which is the one I think you are using)).

 

If so, I'd have to look up the details. However, the wiki article here may be of help.

 

About the trace, you have split up the metric as [math]g_{\mu \nu} = \eta_{\mu \nu} + \kappa h_{\mu \nu}[/math]. You raise and lower indices with the [math]\eta_{\mu \nu}[/math] "bit". So

 

[math]Tr M = \eta^{\nu \mu} M_{\mu \nu}[/math].

 

The details of various gauges, the linear approximation and gravitational radiation can be found in Carroll's lecture notes. I think what you need is in there.

 

The nomenclature transverse traceless comes from the fact that (in a particular gauge) the components of the perturbation are traceless and perpendicular to the wave vector.

Edited March 3, 2010 by ajb