The Algebraic Page Curve

Understand

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.