# Is the equivalence principle in General Relativity an approximation?

I read in web that Einstein used the principle of equivalence to explain General Relativity but we know the gravitation is approximately equal in all of rested frame in gravitional field. In contrary, we can only create uniform acceleration inside a frame if we move it in a direction (The same $a$ will be gotten in each point of the frame ) .

Is it possible to create exact equivalence between accelerated frame and rested frame in gravitational field?

How can the general relativity explain the difference?

• It is exact, but holds for infinitesimal 'chunks' of spacetime only. Because of the curved nature of spacetime, many intuitive notions only hold infinitesimally, where we can approximate the manifold as flat spacetime.
– Danu
Oct 7, 2013 at 9:31