The strict equivalence between gravity and inertial acceleration means that freefalling frames are completely equivalent to inertial frames. Matter, in turn, tells spacetime how to curve. Geometry is related to matter and energy through Einstein's equation. Matter and energy determine inertial frames, but within an inertial frame there is no influence by any outside matter. Thus Mach's principle is present more in spirit than in actuality in the general theory of relativity.
Tidal forces prevent a perfect equivalence of freefall and gravity.
If the gravitational field diverges over the size of an object, the various parts of the object will be pulled by different amounts or in different directions. These differential effects are known as tidal forces. The equivalence principle requires only that the size of the inertial frame be sufficiently small that tidal forces are negligible. General Relativity predicts the bending of light by gravity, gravitational time dilation and length contraction, gravitational redshifts and blueshifts, the precession of Mercury's orbit, and the existence of gravitational radiation. All these effects have been measured, although gravitational radiation has been observed only indirectly via the decay of the orbits of binary pulsars.