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Thread Subject:
Schwarzschild Metric into the Ricci Tensor

Subject: Schwarzschild Metric into the Ricci Tensor

From: Philosophaie

Date: 30 Dec, 2008 02:40:03

Message: 1 of 1

Looking for the Schwarzschild Solution for this equation:
ds^2 = -A(r) / c^2 * dr^2 – r2 / c2 *(d\\theta^2 +(sin d\\phi)^2) + B(r) * dt2
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:
g_ab ; g^ab ; G^c_ab
Ricci Tensor is:
R_bc = R^a_bca = \\Gamma^a_dc * \\Gamma^d_ba – \\Gamma^a_da * \\Gamma^d_bc + \\Gamma^a_ba,c - \\Gamma^a_bc,a
My solution is a 4x4 zero matrix with:
R_11 = 1 / (r^2 * (-r+2*m)^2) *m^2 + 1/(r^2 * (-r+2*m)^2) *m – 1/(r * (-r+2*m)^2) *m
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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