Rindler Wedge

The Rindler wedge is the region of flat (Minkowski) spacetime that a uniformly accelerating observer can ever send signals to or receive signals from. Although special relativity is usually introduced with observers moving at constant velocity, it applies equally to constant acceleration, and that case reveals something surprising: an accelerating observer is cut off from part of spacetime by a horizon, much like the event horizon of a black hole.

Accelerated observers and Rindler coordinates

Consider an observer who accelerates at a constant proper acceleration a forever. In a spacetime diagram, the observer's worldline is a hyperbola, not a straight line. The family of all such hyperbolic worldlines fills only one quarter of the diagram — the wedge defined by x > |ct|. This quarter is the Rindler wedge, and the coordinates adapted to the accelerating observer (in which their motion looks stationary) are called Rindler coordinates.

The boundary of the wedge, the lines x = ±ct, forms the Rindler horizon. Light emitted from beyond this boundary can never catch up to the eternally accelerating observer, so events on the far side are causally hidden from them. The horizon is observer-dependent: it exists because of the observer's motion, not because of any matter or curvature.

Why the Rindler wedge matters

The Rindler wedge is the simplest laboratory for studying horizons. Because the spacetime is flat and contains no gravity, any effect that appears here must come purely from acceleration and the causal structure it creates. This makes it the natural setting for the Unruh effect, in which an accelerating observer perceives the ordinary vacuum as a warm thermal bath. The mathematics of the Rindler horizon closely parallels that of a true black-hole horizon, which is why the wedge is a standard stepping stone toward understanding Hawking radiation and the black-hole information question.

A common misconception

The Rindler horizon does not trap anything in an absolute sense. An inertial observer floating nearby sees no horizon at all and can move freely across the boundary line. The horizon is a feature of one observer's particular acceleration, and it disappears the moment that observer stops accelerating — a key difference from the horizon of a black hole, which is built into the spacetime geometry itself.