constant Jacobian transformation of an inertial frame
Suppose we do a constant Jacobian transformation (NOT Lorentz) of an
inertial frame. This defines a noninertial field with a constant metric in
which the acceleration vector is NONZERO. But this directly contradicts
the geodesic  metric equation. According to this equation, the acceleration
vector is ZERO, because the metric is constant and so it has zero partial
derivatives which make the metric connection zero.
Can anyone explain this direct contradiction?
