Information in, on, and from the Spacetime

Information theory has become increasingly more prominent in physics research, and it is no different in gravity. In this thesis we look at several connections between information and the spacetime. Motivated in part by the black-hole information paradox, we complete a proof of an asymptotic entropy bound and consider the equivalence principle, both in attempt to answer where information may hide IN asymptotically flat space-times. We consider information bounds IN Riemann flat empy regions and ON the null conformal boundary. Our results led us to investigate the physical principles that render potential information at infinity unobservable and consider a communication protocol illustrating a connection between information and energy. We were able to show that quantum effects can account for unobservability of asymptotic charges.Holography is the idea that all the information about a spacetime is contained ON a lower dimensional surface (usually the boundary). Its most concrete realization, AdS/CFT, has already revolutionized physics. Still, that has not stopped physicists from seeking suitable generalizations, and it is in this context that holographic screens were introduced. The causal future of a spacetime region, is the subset of the spacetime where information from that region can reach. A certain characterization of the boundary of the future was needed for proving a new area theorem for holographic screens. We provide a proof of this characterization.Entanglement entropy provides a way of quantifying how information is spread in a quantum system. However, entanglement entropy alone does not provide an exhaustive picture of the distribution of information in a quantum system, and so several other entanglement measures have been studied, including, for instance, entenglement of distillation, entanglement of formation, and entenglament of purification. In many cases, holography provides an efficient way of studying entanglement measures. This allows us to learn about information properties of quantum systems FROM the spacetime. We study potential holographic duals for entanglement of purification and its multipartite generalization, and prove several of their properties