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Einstein–Rosen waves and the Geroch group

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/5.0061929· OSTI ID:1839904
 [1]
  1. Institute for Advanced Study, Princeton, NJ (United States); Institute for Advanced Study
+ Show Author Affiliations
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. Furthermore, our derivation has a straightforward extension to gravitational pulse waves.
Research Organization:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0009988
OSTI ID:
1839904
Journal Information:
Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 62; ISSN 0022-2488
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (12)

Weyl metrics and Wiener-Hopf factorization journal May 2020
Twistor Actions for Integrable Systems journal September 2021
Zur Theorie bin�rer Gravitationsfelder journal December 1925
Inverse scattering and the Geroch group journal February 2013
On gravitational waves journal January 1937
Tau functions and the twistor theory of integrable systems journal February 2000
A Method for Generating New Solutions of Einstein's Equation. II journal March 1972
The Geroch group and non-Hausdorff twistor spaces journal February 1988
Energy of Infinitely Long, Cylindrically Symmetric Systems in General Relativity journal April 1965
Asymptotic structure of symmetry-reduced general relativity journal January 1997
Behavior of Einstein-Rosen waves at null infinity journal January 1997
Reality of the Cylindrical Gravitational Waves of Einstein and Rosen journal July 1957

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Complex analysis
Complex functions
Einstein field equations
General relativity
Gravitational waves
Laurent series expansion
Minkowski space
Recurrence relations
Vector fields