A dynamical mechanism for the Page curve from quantum chaos

If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. We show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. One key feature which leads to the Page curve is the possibility of dynamical processes where operators which make up the reduced density operator of a black hole can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. We conjecture that void formation may provide a microscopic explanation for the recent semi- classical prescription of including islands in the calculation of the entanglement entropy of the black hole radiation.