81 citations · 175 across the 30 of their papers we have counts for
30 papers
Sachs Equations and Plane Waves VI: Penrose Limits
Jonathan Holland, George Sparling
Let be a Lorentzian manifold whose local space of unparametrized null geodesics is smooth. We show that its Penrose limits assemble into a smooth bundle of pla…
Sachs equations and plane waves IV: projective differential geometry
Jonathan Holland, George Sparling
This article gives an invariant representation of the curvature of a plane wave spacetime in terms of the Schwarzian of a curve in the Lagrangian Grassmannian. It develops a genera…
Sachs equations and plane waves III: Microcosms
Jonathan Holland, George Sparling
This article examines the structure of plane wave spacetimes (of signature , ) that are homogeneous (the isometry group is transitive) and geodesically complete --…
Sachs equations and plane waves II: Isometries and conformal isometries
Jonathan Holland, George Sparling
This article describes the symmetries of plane wave spacetimes in dimension four and greater. It begins with a description of the isometric automorphisms, and in particular the hom…
Sachs equations and plane waves, I: Rosen universes
Jonathan Holland, George Sparling
This article, the first in a series, analyzes the general theory of plane wave spacetimes. Following Dmitri Aleekseevsky, these are defined as spacetimes admitting a group of dilat…
Incompleteness Theorems for Observables in General Relativity
Aristotelis Panagiotopoulos, George Sparling, Marios Christodoulou
The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable on…