UC Berkeley

Evidence has been gathering over the decades that spacetime and gravity are best understood as emergent phenomenon, especially in the context of a unified description of quantum mechanics and gravity. The Quantum Focussing Conjecture (QFC) and Quantum Null Energy Condition (QNEC) are two recently-proposed relationships between entropy and geometry, and energy and entropy, respectively, which further strengthen this idea.

In this thesis, we study the QFC and the QNEC. We prove the QNEC in a variety of contexts, including free field theories on Killing horizons, holographic theories on Killing horizons, and in more general curved spacetimes. We also consider the implications of the QFC and QNEC in asymptotically flat space, where they constrain the information content of gravitational radiation arriving at null infinity, and in AdS/CFT, where they are related to other semiclassical inequalities and properties of boundary-anchored extremal area surfaces. It is shown that the assumption of validity and vacuum-state saturation of the QNEC for regions of flat space defined by smooth cuts of null planes implies a local formula for the modular Hamiltonian of these regions. We also demonstrate that the QFC as originally conjectured can be violated in generic theories in \(d\geq5\), which led the way to an improved formulation subsequently suggested by Stefan Leichenauer.