Spacetime Structures of Accelerated Reference Frames in a Deformation-Field Formalism

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 $g=A^T\eta A=P^T\eta P$, while the complete field defines the natural pullback connection $\Gamma [A]=A^{-1}\bar \nabla A$. Standard accelerated frames are treated as integrable Jacobian branches generated by the global motion of the reference frame. Consequently $\Gamma[A]=\mathring\Gamma[g]$, $D=\Gamma[A]-\mathring\Gamma[g]=0$, 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.