I Left-right arrow in Einstein equation

AI Thread Summary
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.
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.]
1617491248432.png

Does it just mean the last term repeated, except this time with ##a## and ##b## indices exchanged? Thanks.
 
Physics news on Phys.org
LHS is symmetric as for a nd b so RHS is also. So your thought seems reasonable.
 
Why is this thread on the Last week's most popular topics list?
 
I am following someone on Youtube who has built a rocket shaped (4 proprllers) drone for the world speed record ... He was having problems with internal heat from electical control gear and battery inside the sealed rocket (about 1kw waste heat) Speed is 500km/hr , I suggested a 4mm hole in the tip of the nose and 8mm hole at rear which should alow sufficient air cooling .. I said this will increase thrust because the air exiting is hotter .. a bit similar to a ram jet ... was I correct...
Back
Top