Radiation from a collapsing object is manifestly unitary

Area of Science:

• Theoretical physics
• Quantum gravity
• Black hole thermodynamics

Background:

• Gravitational collapse is theorized to produce thermal radiation.
• Hawking's initial model of this radiation used a density matrix with only diagonal terms.
• The unitarity of black hole evaporation remains a key theoretical challenge.

Purpose of the Study:

• To investigate the nature of thermal radiation emitted during gravitational collapse.
• To determine if the radiation density matrix corresponds to a pure or mixed state.
• To analyze the role of off-diagonal correlation terms in the density matrix.

Main Methods:

• Explicit mathematical calculations of the radiation density matrix.
• Analysis of both diagonal and off-diagonal terms.
• Comparison of the trace of the density matrix squared over time.

Main Results:

• The density matrix, including off-diagonal correlations, describes a pure state.
• Off-diagonal terms grow over time, significantly modifying the density matrix.
• The trace of the total density matrix squared remains unity, unlike Hawking's approximation.

Conclusions:

• The process of thermal radiation from gravitational collapse is unitary.
• The inclusion of off-diagonal correlations is crucial for understanding the purity of the radiation state.
• This resolves paradoxes related to information loss in black hole evaporation.