81 citations · 175 across the 30 of their papers we have counts for
15 papers · 1 filter
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, 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…
Cosmology: macro and micro
Jonathan Holland, George Sparling
A new approach to cosmology and space-time is developed, which emphasizes the description of the matter degrees of freedom of Einstein's theory of gravity by a family of Kähler-Ein…
The cosmology of a fundamental scalar
Jonathan Holland, George Sparling
We observe that the standard homogeneous cosmologies, those of Minkowski, de Sitter, and anti-de Sitter, which form the matrix for the Robertson--Walker scale factor, live naturall…