Light Rays, Singularities, and All That

Abstract

This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics that was held at the IAS as well as the New Zealand Mathematical Research Institute summer school held in Nelson in January, 2020.

104 pp. V2: Various corrections/improvements, especially in Appendix C. New Appendix D added, V3: minor corrections and improvements to figures., V4: minor corrections and another new Appendix, V5,V6: minor corrections

References in corpus (3)

• Achronal averaged null energy condition
• Fermi Coordinates and Penrose Limits
• The Boundary of the Future

Cited by in corpus (31)

• Humanly traversable wormholes
• Aspects of The First Law of Complexity
• Causal Structures and Nonlocality in Double Holography
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Towards precision holography
• Bounds on quantum evolution complexity via lattice cryptography
• Holographic cameras: an eye for the bulk
• Modular Commutators in Conformal Field Theory
• Generalised Ellis-Bronnikov wormholes embedded in warped braneworld background and energy conditions
• Conformally invariant averaged null energy condition from AdS/CFT
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter
• Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids
• Holographic scattering and non-minimal RT surfaces
• Singularity theorems in the effective field theory for quantum gravity at second order in curvature
• Consequences of using a smooth cosmic distance in a lumpy universe: I
• The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
• The art of building a smooth cosmic distance ladder in a perturbed universe
• Subadditive Average Distances and Quantum Promptness
• Deriving the Gibbons-Maldacena-Nunez no-go theorem from the Raychaudhuri equation
• On the Structure of Black Bounces Sourced by Anisotropic Fluids
• Emergence of smooth distance and apparent magnitude in a lumpy Universe
• Geodesics in Generalised Ellis-Bronnikov Spacetime Embedded in Warped 5D Background
• Einstein's hole argument and Schwarzschild singularities
• Quantum-Gravitational Null Raychaudhuri Equation
• Multiresolution quantum field theory in light-front coordinates
• A proof of Generalized Connected Wedge Theorem
• Raychaudhuri Equation in Kaluza Klein space time
• Positive Mass in General Relativity Without Energy Conditions
• Black holes and their horizons in semiclassical and modified theories of gravity
• Recent Developments in the Penrose Conjecture
• Probing Penrose-type singularities in sonic black holes