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I have to calculate the gravitational field strength g given by the De Sitter-Schwarzschild spacetime.

If G=c=1 I get:

[itex]R_{00}\simeq -kT_{00}+\frac{1}{2}kT\eta_{00}+\Lambda \eta_{00}\simeq [/itex]

[itex]-kT_{00}+\frac{1}{2}kT_{00}\eta^{00}\eta_{00} +\Lambda \eta_{00}\simeq -\frac{1}{2}kT_{00}+ \Lambda =-\frac{1}{2}k\rho+ \Lambda [/itex]

On the other side:

[itex]R_{00}\simeq -\Gamma_{00,j}^j \simeq -\frac{1}{2}\bigtriangledown^2g_{00}\simeq -\bigtriangledown^2 \phi[/itex]

Equaling:

[itex]\bigtriangledown^2 \phi=\frac{1}{2}k\rho-\Lambda=4piG\rho-\Lambda [/itex]

The first problem I have is that I don't know how to get this result in normal units, and the second problem is that, from here, I have to find the gravitational field strength g, and I don't know how to do it.

thanks for any help!

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# Weak field newtonian limit

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