Superluminal Transformations in Spacetimes of Definite Metric

This paper reviews and extends an approach to superluminal kinematics set forth by R. Sutherland and J. Shepanski in 1986. This theory is characterized by a spacetime with positive definite metric, a Lorentz factor of the form $1\mathrm{/}\sqrt{{\beta }^2-1}$, and real-valued proper times and proper lengths for superluminal reference frames.