Seminars: T. A. Rusalev, Entanglement entropy and the problem of information loss in Hawking radiation of black holes

SEMINARS


Seminar by V. V. Kozlov, S. V. Kozyrev, A. S. Trushechkin and I. V. Volovich "Quantum mathematical physics" September 17, 2025 19:35, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)

Entanglement entropy and the problem of information loss in Hawking radiation of black holes T. A. Rusalev
Abstract: The talk will present results on studying the time evolution of entanglement entropy in curved spaces. In Jackiw-Teitelboim gravity with a positive cosmological constant and reflecting boundaries dividing spacetime into a "cosmological system" and a "black hole system", for free Dirac fermions in the vacuum state, the entanglement entropy of the reduced state corresponding to the union of spacelike curves is considered within the island formula framework. It is established that an island configuration exists for the "black hole system" and is absent for the "cosmological system". In the first case, this leads to saturation of the entanglement entropy at the level of the thermodynamic entropy of the horizon, whereas in the second case, depending on the boundary location, the entanglement entropy can take arbitrarily large values. It is shown that in the presence of a reflecting boundary, the entanglement entropy of free Dirac fermions in Schwarzschild spacetime grows in time and reaches saturation, the magnitude of which is determined by the boundary position. It is shown that the generalized entropy for a simply connected symmetric island does not exist for all time values. It is shown that without including the island configuration, the entanglement entropy of free Dirac fermions corresponding to bounded regions of spacelike hypersurfaces in Schwarzschild spacetime grows with time and reaches saturation. An upper bound is indicated, expressing a necessary condition for unitary evolution for the considered regions. It is established that for sufficiently large regions, the saturation value of entropy without an island exceeds it, and accounting for a nontrivial island configuration does not prevent exceeding the upper bound.