2024/03/14 by César Gómez, Gomez, Cesar
Engineering · #Advanced Numerical Analysis Techniques #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2403.09165
openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 II1 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 II1 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.