Ehlers group

In mathematical physics, the Ehlers group, named after Jürgen Ehlers, is a finite-dimensional transformation group of stationary vacuum spacetimes which maps solutions of Einstein's field equations to other solutions. It has since found a number of applications, from use as a tool in the discovery of previously unknown solutions to a proof that solutions in the stationary axisymmetric case form an integrable system.^[1]

^ The original articles are Ehlers, J. (1957), "Konstruktionen und Charakterisierung von Lösungen der Einsteinschen Gravitationsfeldgleichungen", Dissertation, Hamburg University and Geroch, R. (1971), "A method for generating new solutions of Einstein's field equation. I", J. Math. Phys., 12 (6): 918–924, Bibcode:1971JMP....12..918G, doi:10.1063/1.1665681; for the applications, Mars, Marc (2001), "Space-time Ehlers group: Transformation law for the Weyl tensor", Class. Quantum Grav., 18 (4): 719–738, arXiv:gr-qc/0101020v1, Bibcode:2001CQGra..18..719M, doi:10.1088/0264-9381/18/4/311, S2CID 16943248.

[1] The original articles are Ehlers, J. (1957), "Konstruktionen und Charakterisierung von Lösungen der Einsteinschen Gravitationsfeldgleichungen", Dissertation, Hamburg University and Geroch, R. (1971), "A method for generating new solutions of Einstein's field equation. I", J. Math. Phys., 12 (6): 918–924, Bibcode:1971JMP....12..918G, doi:10.1063/1.1665681; for the applications, Mars, Marc (2001), "Space-time Ehlers group: Transformation law for the Weyl tensor", Class. Quantum Grav., 18 (4): 719–738, arXiv:gr-qc/0101020v1, Bibcode:2001CQGra..18..719M, doi:10.1088/0264-9381/18/4/311, S2CID 16943248.

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