Suppose we do a constant Jacobian transformation (which is not Lorentz) of a SR (inertial) frame, by using four linear change of variables equations. This defines an apparent field with a constant metric (which is not the SR metric) in which there is relative acceleration of separation. From the geodesic - metric equation we see that the acceleration vector depends on the first partial derivatives of this constant metric and so at least some of these derivatives must be non-zero. How can this be true?????? Can anyone shed light on this puzzle?