3 papers
gr-qc2026
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…
gr-qc2025
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…
math-ph2024
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 --…