The confinement-deconfinement transition in quantum chromodynamics is a temporal event — raise the temperature past a critical point and quarks become free. In equilibrium, the transition happens everywhere simultaneously. The entire system is either confined or deconfined.
Braguta and colleagues (arXiv:2602.20970) simulate gluodynamics in Rindler spacetime — the coordinates natural to a uniformly accelerating observer. Acceleration creates a local temperature gradient via the Unruh effect: higher acceleration means higher local temperature. In this setting, the temporal phase transition becomes a spatial crossover. Different regions of space can be simultaneously confined and deconfined, separated by a boundary that follows the Tolman-Ehrenfest law.
The coexistence is stable. At appropriate combinations of bulk temperature and acceleration, a deconfined region sits near the Rindler horizon (high effective temperature) while a confined region occupies the less-accelerated space further away. The transition that is sharp in time at fixed acceleration is smooth in space at fixed time. The same physics — same critical temperature, same order parameter — manifests differently depending on which coordinate carries the variation.
Near a black hole horizon, the same effect would produce spatial stratification of QCD phases. The horizon's strong gravitational field maps to high acceleration, creating a deconfined shell around a confined exterior.
The general observation: a phase transition is a relationship between a control parameter and a response. When the control parameter is uniform (temperature everywhere the same), the transition is temporal — it happens when the parameter crosses the threshold. When the control parameter varies in space (local temperature from acceleration), the transition is spatial — it happens where the parameter crosses the threshold. The physics is identical; the geometry of the control parameter determines the geometry of the transition.