In terms of general relativity, what does this question mean?
Does it mean "why does an object feel a force acting on it"?
One object? Which object?
Well, I found this question in the http://en.wikipedia.org/wiki/Acceleration" [Broken] topic in Wikipedia, and I was confused about its meaning.
I don't know what they mean by "equivalent frames of reference", but in GR still only inertial frames have the same physical laws: local experiments give the same results in all of them. The new thing in GR is that free falling frames in a small region of a gravitational field are considered inertial too, so you can use SR there.
So GR is not making accelerated frames equivalent to inertial ones, but it redefines what an inertial vs. accelerated frame is, regarding gravitational fields.
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