Recent Progress in Quantum Gravity: Karch-Randall Braneworld, Entanglement Islands and Graviton Mass

Thesis (Ph.D.)--University of Washington, 2022In this thesis, we review important recent progress in our understanding of entanglement islands and quantum gravity. We illustrate the concept of entanglement island and its implications to the black hole information paradox using the so called KR braneworld, which provides the only existing calculable models of entanglement island in higher spacetime dimensions ($D \geq 2 + 1$). Then we point out that the physics of the Karch-Randall braneworld motivates us to formulate a conjecture that, at the fine grained level, a large class of entanglement islands can exist only in massive gravity theories. We provide evidence supporting our conjecture by showing the absence of entanglement islands in a deformed KR braneworld model where the graviton is massless. At the end, we provide a general proof of our conjecture for a broad class of spacetimes (with dimension $D \geq 2 + 1$), which include asymptotically Anti-de Sitter spacetimes, using Gauss’ law