Investigating Holography: Traversable Wormholes and Closed Universes

In this thesis we study three recent and overlapping developments in the subject of holography: traversable wormholes, quantum extremal islands, and holographic models of closed universes. We construct a traversable wormhole from a charged AdS black hole by adding a coupling between the two boundary theories. We investigate how the effect of this deformation behaves in the extremal limit of the black hole and show that under certain conditions the wormhole can be made traversable even in the extremal limit. Next, we use braneworlds in three-dimensional multiboundary wormhole geometries as a model to study the appearance of entanglement islands when a closed universe with gravity is entangled with two non-gravitating quantum systems. We show that the entropy of the mixed state in the closed universe is bounded by half of the coarse-grained entropy of the effective theory on the braneworld. For large values of the tension T, the worldvolume of a constant-tension brane inside a Schwarzschild-AdS_ black hole is a closed FRW cosmology. However, for d > 2, having a smooth Euclidean solution where the brane does not self-intersect limits the brane tension to T < T_∗, preventing us from realising a separation of scales between the brane and bulk curvature scales. We show that adding interface branes to this model does not relax the condition on the brane tension.