Radiation from a collapsing object is manifestly unitary

Abstract

The process of gravitational collapse excites the fields propagating in the background geometry and gives rise to thermal radiation. We demonstrate by explicit calculations that the density matrix corresponding to such radiation actually describes a pure state. While Hawking's leading order density matrix contains only the diagonal terms, we calculate the off-diagonal correlation terms. These correlations start very small, but then grow in time. The cumulative effect is that the correlations become comparable to the leading order terms and significantly modify the density matrix. While the trace of the Hawking's density matrix squared diverges from unity during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies. This implies that the process of radiation from a collapsing object is unitary.