Principle of Equivalence for non-uniformly accelerated system Consider a frame being accelerated according to the law of gravity, $a=-K/r^2$ where $K$ is some constant and $r$ is measured from some point. Since here the acceleration is exactly the form of gravity, can the equivalence principle be extended to include such non-uniform acceleration and thus extending the applicability of the principle to non-uniform gravitational fields?
PS: I have no familiarity with general relativity, the motivation for this question arises from reading; Kleppner D, Kolenkow R. An Introduction to Mechanics
 A: The equivalence principle holds locally, that is, over domains for which changes in position do not significantly change the reading of an accelerometer. While one can come up with certain arrangements of matter such that certain arrangements of acceleration are indeed indistinguishable, one should be careful with them and not assume sort of extended equivalence principle that holds for all $\vec r$. Consider for example a body at a L1 Lagrange point, whose accelerometer reads zero but which nonetheless is time dilated relative to a point distant from the masses.
With a suitably powerful and well programmed rocket, we could imposed on ourself $a = -K/(r+B)^2$ where r is the displacement from the starting point, $a$ is the proper acceleration (including gravity). But light, causality, and the rest of the universe would not care what our acceleration would be if we went somewhere else. Jeff in his rocket still measures the apple falling on Isaac's head, whatever Jeff's proper acceleration would be if he were flying past the tree.
