Hawking Radiation from Decoherence

It is argued that the thermal nature of Hawking radiation arises solely due to decoherence. Thereby any information-loss paradox is avoided because for closed systems pure states remain pure. The discussion is performed for a massless scalar field in the background of a Schwarzschild black hole, but the arguments should hold in general. The result is also compared to and contrasted with the situation in inflationary cosmology. PACS number: 04.70.-s The process of black-hole evaporation is still not understood on the most fundamental level. One of the key questions concerns the “information-loss paradox” – can a pure quantum state evolve into a mixed state during the evaporation or not [1]? In this Letter I shall argue that Hawking radiation always remains in a pure state and that its mixed appearance emerges through the irreversible process of decoherence [2]. Consider the simplest case of a massless scalar field φ. In the situation of an Unruh observer in Minkowski spacetime one usually considers a hypersurface of constant Rindler time which connects the left with the right Rindler wedge. Tracing out in the Minkowski vacuum the modes of the left part leads to a density matrix in the right part corresponding to a canonical ensemble with temperature a/2π, where a is the acceleration [3]. Alternatively, one can impose the boundary condition φ = 0 at the origin (corresponding to the presence of a “mirror”). In this case the evolution along the right part of constant Rindler time (called t) hypersurfaces is given by the quantum state (denoting the Fourier transform of the scalar field by φ(k)) [4]