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With a classical point particle we have $Gm/r^2$ acceleration, but with a massive object such as a neutron star or black hole we have additional geometrical and time distortions (radial distance increases and local time slows down relative to a distant observer).

What is the formula for gravitational acceleration around a super massive object as a function of distance from its center (defined as equal to circumference/$2\pi$) for an object hovering at rest (relative to the massive body)?

I should be able to convert this myself to a formula of acceleration according to a distant observer but I would still like to know what this is so that I can use it to double check my understanding of how space and time is warped. Since descriptions of how to calculate when something is dense enough to become a black hole use the classical escape velocity, I am guessing that somehow everything will cancel out and it will still end up being $Gm/r^2$.

Sancol.
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Dustin Soodak
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Rob Jeffries found a post that answered most of my question (what is the weight equation through general relativity).

$$accel=\frac{GM}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}$$

where $$r = \frac{circumferenc}{2 \pi}$$

As I guessed, this is just the Newtonian equation divided by time dilation $$\sqrt{1-\frac{2GM}{c^2r}}$$ and assuming that space coordinates are adjusted for radial space expansion. All hovering observers agree on circumference but you have to integrate the following for total (non-relativistic) radial distance traveled: $$\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}$$

One way to look at it is that it is the same acceleration as for the classical case (as pointed out by pavel) except that time runs slower for someone closer to the event horizon so it seems like a higher acceleration to them.

Dustin Soodak
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