The Boundary of the Future

Abstract

We prove that the boundary of the future of a surface $K$ consists precisely of the points $p$ that lie on a null geodesic orthogonal to $K$ such that between $K$ and $p$ there are no points conjugate to $K$ nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

arXiv comment8 pages, 6 figures

References in corpus (7)

• The World as a Hologram
• A Covariant Entropy Conjecture
• Holography in General Space-times
• A Quantum Focussing Conjecture
• A New Area Law in General Relativity
• Proof of a New Area Law in General Relativity
• Generalized Second Law for Cosmology

Cited by in corpus (15)

• Geometry of Complexity in Conformal Field Theory
• A World without Pythons would be so Simple
• Light Rays, Singularities, and All That
• Island Finder and Entropy Bound
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT
• Area Law Unification and the Holographic Event Horizon
• Quantum Penrose Inequality
• Quantum Information Bound on the Energy
• Outer Entropy and Quasilocal Energy
• Holevo Information of Black Hole Mesostates
• Island mirages
• Singularities From Entropy
• Holographic Screen Sequestration
• Cost of holographic path integrals