The Geroch group is an inifinite-dimensional symmetry group of axisymmetric, stationary

Stationary

Stationary can mean:* In statistics and probability: a stationary process.* In mathematics: a stationary point.* In mathematics: a stationary set.* In physics: a time-invariant quantity, such as a constant position or temperature....

 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...

 spacetimes that are solutions of Einstein's equations of general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. It is generated by two non-commuting

Commutativity

In mathematics an operation is commutative if changing the order of the operands does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it...

 subgroups: the Matznerg–Misner group (after Richard Alfred Matzner and Charles W. Misner

Charles W. Misner

Charles W. Misner is an American physicist and one of the authors of Gravitation. His specialties include general relativity and cosmology. His work has also provided early foundations for studies of quantum gravity and numerical relativity....

) of linear combination

Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results...

s (with constant coefficients) of the two Killing vector fields associated with the spacetime's axisymmetry and stationarity, and the Ehlers group

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...

.