- #36
PeterDonis
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Jorrie said:It is also not clear from MTW whether that equation is precise only at the turning points, or everywhere in Schwarzschild coordinates.
It's exact everywhere. It's straightforward to derive that equation from the geodesic equation. I don't have my copy of MTW handy right now, but I'm pretty sure they discuss this.
Jorrie said:Any geodesic that is even slightly 'in-going' at 4M should spiral in, because there is no maximum effective potential below that.
Huh? The maximum effective potential continues to increase all the way down to the (unstable) circular photon orbit at ##r = 3M##.
stevendaryl said:in units where ##c=1##, ##2GM = 1##
I think it should be ##GM = 1##. I don't like units where ##M## disappears from the equations for this reason; ##M## is not a physical constant like ##G## and ##c##, it's a solution parameter, so to me it needs to remain explicit in the equation.