Entanglement entropy of radiation in spherically symmetric black holes

It will be discussed in the talk about the calculation of the entanglement entropy of Hawking radiation for the cases of spherically symmetric four-dimensional eternal Schwarzschild and Reissner–Nordström black holes and its relationship with the information paradox in black hole physics. A verification of the basic properties of the entanglement entropy of the pure state of the entire composite system is given, and it is shown that, generally speaking, these properties are not satisfied. The island formula is used to study the time dependence of the entanglement entropy for various types of finite regions in which radiation is collected. Depending on the size of finite regions, a qualitatively new behavior arises, such as discontinuous evolution of the entanglement entropy, the absence of island formation, the “Cauchy surface breaking” and asymmetric island solutions.