Hawking radiation with pure states

Hawking's seminal work on black hole radiation highlights a critical issue in our understanding of quantum field theory in curved spacetime (QFTCS), specifically the problem of unitarity loss (where pure states evolve into mixed states). In this paper, we examine a recent proposal for a direct-sum QFTCS, which maintains unitarity through a novel quantization method that employs geometric superselection rules based on discrete spacetime transformations. This approach describes a quantum state in terms of components that evolve within geometric superselection sectors of the complete Hilbert space, adhering to the discrete symmetries of a Schwarzschild black hole. Consequently, it represents a maximally entangled pure state as a direct-sum of two components in the interior and exterior regions of the black hole, thereby preserving the unitarity of Hawking radiation by keeping it in the form of pure states.