**Revised Schwarzschild Solution **

**to Accommodate Space Expansion**

__ABSTRACT__** (26 June 2017)**

Deep MOND correlations show far-field gravitation around any spiral galaxy declining inversely with radius, contrary to inverse-radius squared of Newtonian gravitation and general relativity. The required a~1/r theory is obtained by first introducing a fundamentally distinct alternative to relativity physics at the core of special and (therefore) general relativity—specifically, Einstein’s c=constant is replaced by infinite photon-speed radially inward and c/2 radially outward. By itself this step adds terms (e.g., to Maxwell’s equations) without changing predictions. But within Hubble space-expansion, the resulting dΔt′/dt=−VH/c=−rHcH/c2 combined with the Schwarzschild (linearized) time-dilation dΔt′/dt=−GM/rSc2 gives a new, inductively-formulated time-dilation dΔt′/dt=−([GM/rS][rHcH])1/2/c2 which is spatially uniform in uniform fundamental-observer time. Despite this uniform time-dilation in any given epoch, for non-accelerating expansion “−rHcH/c2” becomes the invariant “−rHc(r0H0/rH)/c2” and radial differentiation of “−([GM/rS][r0cH0])1/2/c2” yields non-uniform time-dilation; gravitational acceleration a=d([GM/rS][r0cH0])1/2/dr=−½(GMcH0)1/2/r necessary to explain spiral galaxy rotation flattening analytically follows. Applying the corresponding metric within the Schwarzschild solution gives x10−3 to x10−4 additional gravitational acceleration across the inner planets of the Solar System, which can be reduced by Solar and planetary mass adjustments. Newtonian gravitational acceleration decreases to equal the new gravitational component at ~7000 AU, in accord with recent wide-binary star rotation data, and a~1/r gradually dominates at greater distances where dark matter could be evoked to explain the discrepancy. However, dark matter yields the same a~1/r as Deep MOND around spiral galaxies, and the present deeper theory of gravity, also with a~1/r, may be acceptable due its greater scientific promise—e.g., a new theoretical relationship between time and matter.