Dear Mentz114:
I am greatly indebted to you for your elegant demonstration that there is no Hubble shift in the conformally flat metric ds2=a(t)2[-dt2+dr2]
Because of that I guess I owe it to you to tell you how this metrical question arose in the first place. I'm sure its more than...
I'm only an M.S. in Physics (1967). It will take me days to follow through your calculation.
It does occur to me that ur=0 since the emitter and receiver are both at fixed comoving coordinates and have no radial velocity.
My guess is that yes, n=1/a(t) is likely correct since the...
It is mathematically the same, but it is not physically the same. Below eqn. 8 the authors say:
"Hence the parametric (conformal) time is shown
on clocks that slow down with the expansion
of the universe relative to the clocks showing
cosmic time, and stops in the limit a → ∞...
Yes, that's what it looks like to me too. But frankly so far I've been unable to do the calculation. I am wondering if the entire calculation has to be done in proper time or if the straight line diagonal light lines of conformal time vs. comoving coordinates makes the calculation trivial?
tardy
Yes, but to bring them into that form the scale factor is not a simple function of the time only... it is generally a highly complex function of the time and the space coordinates, specifically the radial coordinate in spherically symmetric solutions. The FLRW expressed in "conformal time" does...
Hello PF:
I noticed a thread on PF in which TOM STOER and others were discussing how to calculate the redshift for an arbitrary metric. I need to talk to Tom if he is still on this list.
The question has arisen in an applied physics field whether the following conformally flat metric...