= Born-rigid front trajectory from a rear worldline
{c}
{title2=$t_H=t_F+\gamma Lv/c^2,\quad x_H=f(t_F)+\gamma L$}
A front worldline at fixed proper distance $L$ along a rear observer's simultaneity slice is parametrized by the displayed equations, with velocity and Lorentz factor evaluated at the rear event. The front time is locally future-oriented when $1+\alpha_FL/c^2>0$, where $\alpha_F$ is the rear signed proper acceleration. At a zero of that factor the rigid coordinate extension encounters an acceleration-horizon obstruction.
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