Cauchy horizon

A Cauchy horizon is a boundary in a spacetime beyond which the initial value problem ceases to be well-posed. Named after Augustin-Louis Cauchy, it marks the limit of predictability: given complete initial data on a spacelike surface, one can predict the future uniquely only up to the Cauchy horizon. Beyond it, new information — potentially infinite in quantity — can enter the system from regions not constrained by the initial data.

Cauchy horizons arise in the maximal extensions of exact solutions to Einstein's equations, most notably the Reissner-Nordström and Kerr-Newman black holes. In these solutions, the inner horizon (the Cauchy horizon) is the boundary between the black hole interior and a region containing closed timelike curves or another asymptotically flat universe. The Chronology Protection Conjecture suggests that quantum effects destabilize Cauchy horizons, converting them into curvature singularities and restoring predictability.

The presence of a Cauchy horizon signals a breakdown of global hyperbolicity and, with it, the clean separation between past and future on which causal physics depends.