In mathematical physics, the Ehlers group, named after Jürgen Ehlers

Jürgen Ehlers

Jürgen Ehlers was a German physicist who made notable contributions to the current understanding of Albert Einstein's theory of general relativity...

, is a finite-dimensional transformation group of stationary vacuum

Vacuum

In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

 spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

s 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

Integrable system

In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems.In the general theory of differential systems, there is Frobenius integrability, which refers to overdetermined systems. In the classical theory of Hamiltonian dynamical...

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