  We derive the metric of an accelerating observer moving with non-constant
proper acceleration in flat spacetime. With the exception of a limiting case
representing a Rindler observer, there are no horizons. In our solution,
observers can accelerate to any desired terminal speed $v_{\infty} < c$. The
motion of the accelerating observer is completely determined by the distance of
closest approach and terminal velocity or, equivalently, by an acceleration
parameter and terminal velocity.
