Looking for the Schwarzschild Solution for this equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]ds^2 = -A(r) / c^2 * dr^2 - r^2 / c^2 *(d\\theta^2 +(sin(\\theta))^2 *d\\phi^2) + B(r) * dt^2[/tex]

where

A(r) = 1 / (1-2*m/r)

And

B(r) = (1-2*m/r)

From this can be calculated the co- and contra-varient metric tensors and Affinity:

[tex]g_{ab}[/tex]

[tex]g^{ab}[/tex]

[tex]\Gamma^{c}_{ab}[/tex]

Ricci Tensor is:

[tex]R_{bc} = R^{a}_{bca} = \Gamma^{a}_{dc}*\Gamma^{d}_{ba} - \Gamma^{a}_{da}*\Gamma^{d}_{bc} + d/dx^{c} * \Gamma^{a}_{ba} - d/dx^{a} * \Gamma^{a}_{bc}[/tex]

My solution is a 4x4 matrix with all zeros except on the diagonal.

My choices for A(r) and B(r) may not be correct for Earthâ€™s orbit and geodesics. Could

someone steer me in the right direction.

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# Ricci Tensor from Schwarzschild Metric

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