### abstract

- A bstract The unitary evaporation of a black hole (BH) in an initially pure state must lead to the eventual purification of the emitted radiation. It follows that the late radiation has to be entangled with the early radiation and, as a consequence, the entanglement among the Hawking pair partners has to decrease continuously from maximal to vanishing during the BH's life span. Starting from the basic premise that both the horizon radius and the center of mass of a finite-mass BH are fluctuating quantum mechanically, we show how this process is realized. First, it is shown that the horizon fluctuations induce a small amount of variance in the total linear momentum of each created pair. This is in contrast to the case of an infinitely massive BH, for which the total momentum of the produced pair vanishes exactly on account of momentum conservation. This variance leads to a random recoil of the BH during each …