Abstract:
The Covariant Entropy Bound implies a singularity in the domain of dependence of hyperentropic regions, i.e., regions whose entropy exceeds their boundary area. This extends the Penrose singularity theorem to a large class of compact regions. The quantum version of the bound implies a similar theorem in settings where quantum effects are dominant, such as a black hole after the Page time. This leads to an interesting puzzle: a “quantum singularity” is predicted in settings where the classical geometry is smooth.