Event Horizon

An event horizon is the boundary of the region of spacetime from which nothing — not matter, not light, not any signal — can escape to infinity. For a non-rotating black hole of mass M it is the sphere at the Schwarzschild radius r_s = 2GM/c², the radius at which the metric factor (1 − r_s/r) vanishes. It is defined globally, by the causal structure of the whole spacetime, rather than by any local measurement: an observer crossing it makes no local measurement that flags the crossing.

Crucially, the horizon is not a material surface and not a true singularity. In the original Schwarzschild coordinates the metric appears to break down at r = r_s, but this is a coordinate artifact — the failure of a particular map, like longitude lines crowding to a point at the Earth's pole. Coordinate-independent curvature scalars (the Kretschmann scalar 12 r_s²/r⁶) are perfectly finite there and diverge only at the central singularity r = 0. Coordinates adapted to infalling light, introduced by Eddington (1924) and Finkelstein (1958), pass smoothly across the horizon and revealed it as a causal boundary, not a wall.

The two perspectives on the horizon are radically different. A distant observer sees an infalling object slow, redden, and freeze at the horizon, its emitted light redshifted to infinity — it never appears to cross. The infalling object itself crosses in finite proper time and, for a sufficiently massive hole, feels nothing remarkable; tidal forces at the horizon scale as 1/M² and are gentle for supermassive holes. Inside, the light cones tip so far that every future-directed path leads to smaller radius: the central singularity becomes a moment in the infaller's future, not a place that can be avoided.

The surface r = r_s appeared in Karl Schwarzschild's 1916 solution but was misread for decades as a physical singularity; Einstein argued in 1939 that it could never form. Georges Lemaître (1933), Arthur Eddington, and David Finkelstein (1958) showed the apparent singularity was a coordinate artifact. John Archibald Wheeler popularized the term 'black hole' in 1967, and the modern global definition of the horizon as a causal boundary was sharpened by Roger Penrose and Stephen Hawking in the late 1960s. The Event Horizon Telescope imaged the silhouette of M87's horizon in 2019 and Sagittarius A's in 2022.