Evolution between slices in D>2 curved spacetimes shifts the state between unitarily inequivalent Fock representations; the physical representation can be fixed locally by a positive-frequency condition equivalent, in leading order, to the Hadamard condition.
The information paradox and the locality bound
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Hawking's argument for information loss in black hole evaporation rests on the assumption of independent Hilbert spaces for the interior and exterior of a black hole. We argue that such independence cannot be established without incorporating strong gravitational effects that undermine locality and invalidate the use of quantum field theory in a semiclassical background geometry. These considerations should also play a role in a deeper understanding of horizon complementarity.
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Challenges for describing unitary evolution in nontrivial geometries: pictures and representations
Evolution between slices in D>2 curved spacetimes shifts the state between unitarily inequivalent Fock representations; the physical representation can be fixed locally by a positive-frequency condition equivalent, in leading order, to the Hadamard condition.