The Geroch group is an infinite-dimensional symmetry group of
axisymmetric
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...
,
stationary
In addition to its common meaning, stationary may have the following specialized scientific meanings:
Mathematics
* Stationary point
* Stationary process
* Stationary state
Meteorology
* A stationary front is a weather front that is not moving ...
vacuum spacetimes
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
that are solutions of
Einstein's equations of
general relativity. It is generated by two
non-commuting subgroups: the
Matzner–Misner group (after Richard Alfred Matzner and
Charles W. Misner) of
linear combinations (with constant coefficients) of the two
Killing vector fields associated with the spacetime's axisymmetry and stationarity, and the
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 numb ...
.
See also
*
Robert Geroch
Robert Geroch (born 1 June 1942 in Akron, Ohio) is an American theoretical physicist and professor at the University of Chicago. He has worked prominently on general relativity and mathematical physics and has promoted the use of category theo ...
Bibliography
*
General relativity
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