A Gravity Tensor and Gauge Equations for Newtonian Dynamics

It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric E and the magnetic B of the Maxwell equations in the electromagnetic field. The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”.