Singularities from Entropy

Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. ???Hyperentropic??? means that the entropy of the region exceeds the Bekenstein-Hawking entropy of its spatial boundary. Our theorem provides a direct link between singularities and quantum information. The hyperentropic condition replaces the non compactness assumption in Penrose???s theorem, so our theorem is applicable even in a closed universe. In an asymptotically de Sitter spacetime, for example, a big bang singularity can be diagnosed from the presence of dilute radiation at arbitrarily late times. In asymptotically flat space, Penrose???s theorem can be recovered by adding soft radiation.