Is the Einstein tensor in 2D or 1+1D always zero? If so, why? I recently installed EinsteinPy and started playing wing different metrics - for the 2D cases the result turned out to be always zero.
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Einstein tensor in 2D is always zero. You can just compute it explicitly (for a generic metric) and verify this. – Prahar Oct 06 '23 at 04:55
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1Duplicate of Einstein's field equations in (1+1) spacetime?, see e.g. references in the linked answer. – Quillo Oct 07 '23 at 05:59
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1Possible duplicates: https://physics.stackexchange.com/q/1417/2451 and links therein. – Qmechanic Oct 07 '23 at 06:56
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Please refer here. From here you will learn that in 2D
$$R_{abcd} = \frac{R}{2}(g_{ac}g_{bd}-g_{ad}g_{cb})$$ Contracting $a$ and $c$ both sides, you will obtain $$R_{bd} = \frac{R}{2}g_{bd} \implies G_{bd} = 0$$
Dr. user44690
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