entropy of the entangled Hawking radiation

Abstract

Entropic information theory, as a unified informational theory, presents a new informational theoretical framework capable of fully describing the evaporation of the black holes phenomenon while resolving the information paradox, reconciling quantum formalism and relativistic formalism in a single approach. With a set of five new equivalent equations expressing entropy, and by introducing the Hawking temperature into one of them, it is possible to solve the black holes information paradox by being able to calculate the entropy of entangled Hawking radiation, entangled with the fields inside black holes, allowing us to extract information from inside black holes. The proposed model solves the information paradox of black holes by calculating a new entropy formula for the entropy of black holes as equal to the entropy of the pure state of entangled Hawking radiation, itself equal to the fine-grained entropy or von Neumann entropy, itself according to the work of Casini and Bousso equal to the Bekenstein bound which is itself equal, being saturated by Bekenstein-Hawking entropy, at this same entropy. Moreover, since the law of the entropy horizon of black holes turns out to be a special case of the Ryu-Takayanagi conjecture, this general formula for the fine-grained entropy of quantum systems coupled to gravity, equalizes the entropy of entangled Hawking radiation with the gravitational fine-grained entropy of black holes, and makes it possible to relate this resolution of the information paradox of black holes based on the concept of mass of the information bit to quantum gravity explaining the emergence of the quantum gravity process through the fundamentality of entangled quantum information.