Acceleration without Horizons

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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∞ < 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.