In the einstein equation

 

[math]R_{uv}-0,5 R g_{uv}+ \Lambda g_{uv} = \frac{8\pi G}{c^4}T_{uv}[/tex][/math]

 

i understand that units of [math]g_{uv}=L^2[/math] and then [math]R=\Lambda=\frac{1}{L^2}[/math]

 

¿[math]R_{uv}[/math] is dimensional less??

 

[math]G=\frac{L^3}{T^2 M}[/math] and [math]\frac{G}{c^4}=\frac{T^2}{M}[/math] then

 

¿¿¿[math]T_{uv}=\frac{M}{T^2}[/math]?????

I think that the metric tensor is dimensionless and that the unit of the Ricci tensor is L^(-2).

By the way, the unit of the stress-energy tensor is the unit of energy per volume.