As stated by Max Born in his famous book,"Einstein's Theory of Relativity",Dover Publications,1962, pgs 344 & 345:
According to GR, we cannot distinguish between a geo or helio / acentric system. The forces require a different formulation, and the universe would need to be configured to support geocentrism, but this can not be ruled out by any evidence we have at this point....Thus we may return to Ptolemy's point of view of a 'motionless earth'. This wiould mean we use a system of reference rigidly fixed to the earth in which all the stars are performing a rotational motion with the same angular velocity around the earth's axis...One has to show that the transformed metric can be regarded as produced according to Einstein's field equations, by distant rotating masses. This has been done by Thirring. He calculated a field due to a rotating, hollow, thick-walled sphere and proved that inside the cavity it behaved as though there were centrifugal and other inertial forces usually attributed to absolute space.
Thus from Einstein's point of view, Ptolemy and Corpenicus are equally right.