Can general relativistic description of gravitation be considered complete?

The local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about -3 x 10(-5). In the solar system, this potential is constant to about 1 part in 10(11). Consequently, planetary orbits, which are determined by the gradient in the gravitational potential, remain unaffected. However, this is not so for the recently introduced flavor-oscillation clocks where the new redshift-inducing phases depend on the gravitational potential itself. On these grounds, and by studying the invariance properties of the gravitational phenomenon in the weak fields, we argue that there exists an element of incompleteness in the general relativistic description of gravitation. An incompleteness-establishing inequality is derived and an experiment is outlined to test the thesis presented.