Relativity: Schwarzschild metric: Ricci tensors

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R₀₀ =
(000) = 0
(001) = - [(g¹¹/2)∂₁g₀₀][(g⁰⁰/2)∂₁g₀₀]
(002) = 0
(003) = 0
(010) = + ∂₁[(g¹¹/2)∂₁g₀₀]0
(011) = + [(g¹¹/2)∂₁g₀₀][(g¹¹/2)∂₁g₁₁]0
(012) = + [(g¹¹/2)∂₁g₀₀][(g²²/2)∂₁g₂₂]0
(013) = + [(g¹¹/2)∂₁g₀₀][(g³³/2)∂₁g₃₃]0
(020) = 0
(021) = 0
(022) = 0
(023) = 0
(030) = 0
(031) = 0
(032) = 0
(033) = 0

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R₁₁ =
(100) = - [(g⁰⁰/2)∂₁g₀₀][(g⁰⁰/2)∂₁g₀₀]
(101) = 0
(102) = 0
(103) = 0
(110) = + [(g¹¹/2)∂₁g₁₁][(g⁰⁰/2)∂₁g₀₀]0
(111) = + ∂₁[(g¹¹/2)∂₁g₁₁]
(112) = + [(g¹¹/2)∂₁g₁₁][(g²²/2)∂₁g₂₂]0
(113) = + [(g¹¹/2)∂₁g₁₁][(g³³/2)∂₁g₃₃]0
(120) = 0
(121) = 0
(122) = - [(g²²/2)∂₁g₂₂][(g²²/2)∂₁g₂₂]
(123) = 0
(130) = 0
(131) = 0
(132) = 0
(133) = - [(g³³/2)∂₁g₃₃][(g³³/2)∂₁g₃₃]

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R₂₂ =
(200) = 0
(201) = 0
(202) = 0
(203) = 0
(210) = + [(g¹¹/2)∂₁g₂₂][(g⁰⁰/2)∂₁g₀₀]0
(211) = + [(g¹¹/2)∂₁g₂₂][(g¹¹/2)∂₁g₁₁]0
(212) = + ∂₁[(g¹¹/2)∂₁g₂₂]0
(213) = + [(g¹¹/2)∂₁g₂₂][(g³³/2)∂₁g₃₃]0
(220) = 0
(221) = - [(g¹¹/2)∂₁g₂₂][(g²²/2)∂₁g₂₂]
(222) = 0
(223) = 0
(230) = 0
(231) = 0
(232) = 0
(233) = - [(g³³/2)∂₂g₃₃][(g³³/2)∂₂g₃₃]

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R₃₃ =
(300) = 0
(301) = 0
(302) = 0
(303) = 0
(310) = + [(g¹¹/2)∂₁g₃₃][(g⁰⁰/2)∂₁g₀₀]0
(311) = + [(g¹¹/2)∂₁g₃₃][(g¹¹/2)∂₁g₁₁]0
(312) = + [(g¹¹/2)∂₁g₃₃][(g²²/2)∂₁g₂₂]0
(313) = + ∂₁[(g¹¹/2)∂₁g₃₃]0
(320) = 0
(321) = 0
(322) = 0
(323) = + ∂₂[(g²²/2)∂₂g₃₃]0
(330) = 0
(331) = - [(g¹¹/2)∂₁g₃₃][(g³³/2)∂₁g₃₃]
(332) = - [(g²²/2)∂₂g₃₃][(g³³/2)∂₂g₃₃]
(333) = 0

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