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In flat space-time the metric is

[itex]ds^2[/itex][itex]=[/itex][itex]-dt^2[/itex][itex]+dr^2+r^2[/itex][itex]\Omega^2[/itex]

The Schwarzschild metric is

[itex]ds^2[/itex][itex]=-[/itex][itex](1-\frac{2MG}{r})[/itex][itex]dt^2[/itex][itex]+[/itex][itex]\frac{dr^2}{(1-\frac{2MG}{r})}[/itex][itex]+[/itex][itex]r^2d[/itex][itex]\Omega^2[/itex]

Very far from the planet, assuming it is symmetrical and non-spinning, the Schwarzschild metric reduces to the flat space-time metric (as [itex]r[/itex] goes to infinity)

Now, from this equation it can be concluded that [itex]g_{00}{}^{}[/itex][itex]=[/itex][itex]1-2GM/R[/itex]

Then, [itex]g_{rr}{}^{}[/itex][itex]=[/itex][itex]\frac{1}{(1-2MG/R)}[/itex]

If I want to get a matrix for this, what are other non-zero components of the metric [itex]g[/itex]?

I also set c=1.

Also, I would like to get components of the Stress-Energy tensor:

[itex]\mathrm T_{}{}^{00}[/itex][itex]=[/itex][itex]\rho[/itex][itex]c^2[/itex]

[itex]\mathrm T_{}{}^{10}[/itex][itex]=[/itex][itex]\rho[/itex][itex]v_{x}{}^{}[/itex]

[itex]\mathrm T_{}{}^{20}[/itex][itex]=[/itex][itex]\rho[/itex][itex]v_{y}{}^{}[/itex]

[itex]\mathrm T_{}{}^{30}[/itex][itex]=[/itex][itex]\rho[/itex][itex]v_{z}{}^{}[/itex]

Please check those which I wrote and add those which I haven't mentioned.

Thanks!