The Unruh state models Hawking radiation with no particles incoming from past infinity. It is the quantum-field state appropriate to an evaporating or collapsing black hole: outgoing radiation reaches future infinity, while the state is vacuum-like for incoming modes at past null infinity.
This distinguishes it from the Hartle–Hawking state, which represents an eternal black hole in thermal equilibrium. Hartle–Hawking radiation contains both outgoing and incoming thermal flux, so it does not describe an isolated black hole losing mass. The Boulware state has no incoming or outgoing particles at infinity but becomes singular at the event horizon, making it unsuitable for a radiating black hole. “Rindler state” refers to uniformly accelerated observers in flat spacetime, not the standard evaporating-black-hole boundary condition.
The state is named for William G. Unruh, whose work connected quantum fields, horizons, and observer-dependent particle definitions. Hawking radiation is predicted to be thermal at large distances, with a temperature inversely proportional to the black hole’s mass; the outgoing energy is balanced by a corresponding loss of black-hole mass.