What is the correct expression for the acceleration of a static test-particle in coordinate time according to the Schwarzshild solution? I am a bit confused. I would like it to be the same as classically, ## d\bar{v}/dt=-\frac{GM}{r^2}\hat{r} ##, but according to "reflections on relativity":

http://www.mathpages.com/rr/s6-04/6-04.htm
The expression for the acceleration of a static test-particle is only the same as classically if you replace coordinate time with proper time, (see equation 6). I am guessing that this means that according to the Schwarzschild solution the acceleration of a static test-particle in coordinate time is

[tex]\frac{d^2 r}{dt^2} =

- \frac{GM / {r^2}} { (1 - {{2GM} {/} {rc^2}}) }

[/tex]

Is this correct? I would like to have it that relativity will only come in to play when the test-particle has started moving but according to the above it will also play a role in the static case...