The Algebraic Page Curve
arxiv(2024)
摘要
The Page curve describing the process of black hole evaporation is derived in
terms of a family, parametrized in terms of the evaporation time, of finite
type II_1 factors, associated, respectively, to the entanglement wedges of the
black hole and the radiation. The so defined Page curve measures the relative
continuous dimension of the black hole and the radiation along the evaporation
process. The transfer of information is quantitatively defined in terms of the
Murray von Neumann parameter describing the change of the spatial properties of
the factors during the evaporation. In the simplest case the generator of the
evaporation process is defined in terms of the action of the fundamental group
of the hyperfinite type II_1 factor. In this setup the Page curve describes a
phase transition with the transfer of information as order parameter. We
discuss the limits of either a type I or a type III description of the black
hole evaporation.
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