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 Earth’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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