Semiclassical Hilbert space of AdS black holes: factorization and fluctuations

In this talk I will discuss the microscopic interpretation of the Hilbert space of AdS black hole according to the semiclassical gravity. I will review the construction of the corresponding microstates and explain how these states help resolve the AdS/CFT Hilbert space factorization puzzle. I will also discuss the extension of the formalism to describe microstates of out-of-equilibrium fluctuations of black holes, represented by infalling shells.