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Sachs equations and plane waves, I: Rosen universes
Jonathan Holland, George Sparling
https://arxiv.org/abs/2402.07036 https://arxiv.…

Sachs equations and plane waves, I: Rosen universes
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 dilations leaving invariant a smooth curve. If this curve is specified as part of the structure, the spacetime is termed a Penrose limit, whose theory was developed first by Roger Penrose. The main result is that every plane wave is a Rosen universe, a generalization of the smooth metrics of Albert Einstein and Nathan Rose…