I Left-right arrow in Einstein equation

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Thread starter etotheipi
Start date Apr 3, 2021
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Einstein Einstein equation

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The left-right arrow notation ##a \leftrightarrow b## in the Einstein equation indicates a symmetry between the indices a and b, suggesting that the last term can be expressed with these indices exchanged. This symmetry implies that the left-hand side (LHS) and right-hand side (RHS) of the equation are equivalent when the indices are swapped. The discussion also highlights the relevance of this notation in understanding the properties of the equation. The inquiry into its meaning reflects a broader interest in the nuances of Einstein's equations. Overall, the notation emphasizes the inherent symmetry in the mathematical formulation.

Apr 3, 2021

etotheipi

Short, probably stupid, question; what does this left-right arrow ##a \leftrightarrow b## at the bottom-right mean? [It's this paper for ref.]

Does it just mean the last term repeated, except this time with ##a## and ##b## indices exchanged? Thanks.

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Apr 3, 2021

anuttarasammyak

Gold Member

LHS is symmetric as for a nd b so RHS is also. So your thought seems reasonable.

Apr 10, 2021

Demystifier

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