This paper develops a deformation-field formalism for accelerated physical reference frames based on a full inertial deformation field A=OP, where O is a Lorentz-orthogonal orientation factor and P is a dilation-shear factor. The induced metric is g=AT A=PT P, while the complete field defines the natural pullback connection A=A^-1 A. Standard accelerated frames are treated as integrable Jacobian branches generated by the global motion of the reference frame. Consequently =, D=-=0, and ordinary geodesics and pullback autoparallels coincide. A relativistic moving-frame construction based on an accelerated worldline and an orthonormal tetrad gives translation and rotation in a single spacetime deformation field, with the familiar nonrelativistic inertial-force law obtained as a limit. Rindler and uniformly rotating frames are recovered as flat non-inertial metric structures, whose light cones, horizons, Sagnac-type anisotropy, and light-cylinder boundaries are determined by g. The formulation clarifies why inertial effects can be represented by integrable frame deformations whereas genuine gravitational deformations are generally only locally equivalent to them.
Gordon Liu (Thu,) studied this question.