How can we prove that in 2D the Ricci scalar is proportional to the Ricci tensor? I started with the second Bianchi identity, set 2 axes equal - and it led me to the fact that in 2D the covariant derivative of the Ricci tensor is zero. However, I cannot prove that the Ricci tensor is proportional to the Ricci scalar from it.
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References for 1+1 GR: https://physics.stackexchange.com/a/773866/226902, possible answers: https://physics.stackexchange.com/a/77990/226902 https://physics.stackexchange.com/q/361333/226902 https://physics.stackexchange.com/q/674975/226902 – Quillo Nov 11 '23 at 16:15
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It doesn’t make sense to say that a tensor is proportional to a scalar. – Ghoster Nov 11 '23 at 17:40
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How is this question any different from your previous duplicate about the Einstein tensor vanishing in 2D? – peek-a-boo Nov 12 '23 at 20:08