Entanglement in gauge/ gravity duality

Abstract

In this thesis, we present studies that elucidate the relationship between entanglement in strongly coupled gauge theories and the geometry of their gravity duals. In the first, we find that in a certain class of time-dependent states which have a gravity dual in which a black hole forms, the entanglement entropy of large regions grows linearly in time, following the growth of certain time-like slices in the interior of the black hole. In the second, we find a unified prescription in the gravity dual for calculating the action of the entanglement Hamiltonian associated to an arbitrary spatial region in a given holographic state. In particular, we find that the linearized perturbation of the metric caused by the entanglement Hamiltonian propagates from the bulk entangling surface.