Acceleration without Horizons

TL;DR

This paper derives the metric for a non-uniformly accelerating observer in flat spacetime, revealing that, unlike Rindler observers, such observers generally do not experience horizons and can reach any speed below light speed.

Contribution

It provides a new exact metric for accelerating observers with non-constant acceleration, expanding understanding beyond the Rindler case.

Findings

Observers can accelerate to any speed below c.

No horizons generally form for non-constant acceleration.

The motion is fully determined by initial distance and terminal velocity.

Abstract

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.