Using 1% of speed of light, it will slow down by 0.005% (That's much less than I expected)
http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=Plot%5B1...
See also [1].
[1] http://www.edu-observatory.org/physics-faq/Relativity/SR/clo...
Not from acceleration, from depth in a gravitational potential well. See my other posts upthread.
I don't know what that formula looks like.
The white star has non-trivial mass of its own which greatly complicates the curvature of the local space-time region and render the Kerr-Metric equations lacking.
GR is really complicated FYI.
Unless the hole is rotating extremely rapidly (which I don't see mentioned), the difference between the Kerr metric and the Schwarzschild metric (which is what I used for the formula I posted upthread) is too small to matter unless you are really close to the hole's horizon.
The paper guesses that the black hole is ~ 1 solar mass, so the Schwarzschild radius would be about 3 km.
The distance is about 2.5x the earth-moon, which is about 10^6 km.
btw, paper here: https://arxiv.org/pdf/1702.02167.pdf
sqrt(1 - 2M/r - v^2)
instead of
sqrt(1 - v^2)
(where I am using units where G = c = 1). For an object in a free-fall circular orbit, v^2 = M/r, so the above formula can be simplified to
sqrt(1 - 3M/r)
Yes, but doesn't that ignore the gravitational
acceleration
What we perceive as gravitational acceleration is just objects traveling in straight lines (at constant speeds) though 4D space-time. Circular orbits are just straight lines of constant velocity bent around by the local curvature of space-time (which can be caused by a local density of mass-energy).
The idea of acceleration assumes a force is acting on a body. Gravity isn't a force in General Relativity. It is the shape of the universe.
A better way of stating this would be that objects moving solely under gravity have zero acceleration in GR, because in GR, acceleration means proper acceleration--what is measured by an accelerometer. Objects moving solely under gravity are in free fall.
> All bodies are stationary in GR and observe other things moving in reference to themselves.
This isn't correct. There is no requirement that an observer in GR must use coordinates in which they are at rest.
That's not correct. Gravitational time dilation isn't a function of acceleration, it's a function of gravitational potential, i.e., how deep you are in the potential well of the source.
(Also, an object that is in a free-fall orbit has zero acceleration in GR, since in GR acceleration is proper acceleration--what is measured by an accelerometer.)