Abstract

The covariant holographic entanglement entropy formula proposed by Hubeny, Rangamani, and Takayanagi asserts that the entropy of a boundary region is given by the area of a certain extremal spacelike surface in the bulk. Unlike for more familiar objects like timelike geodesics and horizons, there are not yet many theorems about extremal spacelike surfaces in the general-relativity literature. However, based on considerations from quantum information theory, the HRT formula implies or suggests a large number of interesting general statements about such surfaces and their relation to the spacetime’s global causal structure. The effort to prove these novel conjectures has spurred significant recent developments in GR. I will explain the conjectures, their motivation, and the progress that has been made toward proving them.