Einstein-Rosen Waves and the Geroch Group

Abstract

Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to pure algebra. In this short note, we use these facts to give a purely algebraic derivation of the Einstein-Rosen metric, which describes a cylindrical gravitational wave. Our derivation has a straightforward extension to gravitational pulse waves.

9 pages

References in corpus (6)

• Asymptotic Structure of Symmetry Reduced General Relativity
• Selected solutions of Einstein's field equations: their role in general relativity and astrophysics
• Behavior of Einstein-Rosen Waves at Null Infinity
• Inverse Scattering and the Geroch Group
• Weyl metrics and Wiener-Hopf factorization
• Tau-functions, twistor theory, and quantum field theory

Cited by in corpus (7)

• Twistor Actions for Integrable Systems
• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Riemann-Hilbert problems, Toeplitz operators and ergosurfaces
• Generating new gravitational solutions by matrix multiplication
• Classical integrability in the presence of a cosmological constant: analytic and machine learning results
• Cylindrical Gravitational Waves in Einstein-Aether Theory
• Solving gravitational field equations by Wiener-Hopf matrix factorisation, and beyond