Physics and Astronomy Department

Brigham Young University,

Provo, Utah 84602, U.S.A.

E-mail: bkentharrison@attbi.com, bkh@byu.edu

**Applications of symmetry to general relativity**

**Abstract:**

The equations of general relativity are highly nonlinear partial differential
equations and require special techniques to solve exactly. Symmetry
considerations have sometimes helped find solutions. Three examples
will be considered here. The first considers a scaling symmetry in
the equations for spherical symmetry with a perfect fluid, which is of
historical importance in understanding neutron stars and black holes.
The second involves symmetries in the Ernst equation for stationary axially
symmetric fields, which are related to the methods worked out in the 1970s
for finding solutions to that equation. The third example is an ongoing
investigation into critical gravitational collapse, a topic of current
interest, using a symmetry of the equations and other analytic techniques.