That's okay, I don't know anything about Fermi normal coordinates, and I've only used Rindler coordinates once.
I was confused since I thought I could just construct Minkowski coordinates for Simon (corresponding to the proper distances and proper times which they don't) but he's not...
v=\frac{1}{1-2 \mu/r} \frac{dr}{dt} then gives that result doesn't it (applying the geodesic equations to Ed who follows a geodesic). Is it the case that in the neighbourhood of Simon the metric I suggest holds, but only extremely locally?
Okay, so then in Simon's small patch of the spacetime, he sees Ed go past at drs/dts.
How does Simon perameterize the invariant ds2. Is it even the same 'invariant' as Ed's?
And I still don't quite understand why you can't write
dts2 - drs2 ≈ ds2 = (1-2μ/r) dt2 - (1- 2μ/r)-1 dr2 , to...
Yes that's what I thought, but if one solves the geodesic equations you find dr/dτ = -√2μ/r. If instead of perameterizing the metric in terms of τ, we instead use the proper time and proper distance of Simon then we find the corresponding derivative drs/dts = -√2μ/r, I found this in a bunch of...
Hello,
The following has been confusing my friends and I, I want to make sure I have this clear as it is fairly elementary. (note set c = 1)
Ed is falling radially into a black hole, the Schwarzschild metric is:
ds2 = (1-2μ/r) dt2 - (1- 2μ/r)-1 dr2
his proper time is dτ2 = (1-2μ/r) dt2 -...
Hi,
I was wondering if the stars in a galaxy are orbiting its centre with (for example) 'anticlockwise' angular momentum. Then would you expect the orbits of the galaxy around the centre of a galactic cluster (if it's in one) to be 'clockwise' or 'anticlockwise' or will it not make much...