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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