Brinkmann coordinates
![]() | This article may be too technical for most readers to understand.(April 2020) |
Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. They are named for Hans Brinkmann. In terms of these coordinates, the metric tensor can be written as
where , the coordinate vector field dual to the covector field , is a null vector field. Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars. Physically speaking, it serves as the wave vector defining the direction of propagation for the pp-wave.
The coordinate vector field can be spacelike, null, or timelike at a given event in the spacetime, depending upon the sign of at that event. The coordinate vector fields are both spacelike vector fields. Each surface can be thought of as a wavefront.
In discussions of exact solutions to the Einstein field equation, many authors fail to specify the intended range of the coordinate variables .[citation needed] Here we should take
to allow for the possibility that the pp-wave develops a null curvature singularity.
References
- Stephani, Hans; Kramer, Dietrich; MacCallum, Malcolm; Hoenselaers, Cornelius & Herlt, Eduard (2003). Exact Solutions of Einstein's Field Equations. Cambridge: Cambridge University Press. ISBN 0-521-46136-7.
- H. W. Brinkmann (1925). "Einstein spaces which are mapped conformally on each other". Math. Ann. 18: 119–145. doi:10.1007/BF01208647.
- Justapedia articles that are too technical from April 2020
- Articles with invalid date parameter in template
- All articles that are too technical
- All articles with unsourced statements
- Articles with unsourced statements from April 2020
- Coordinate charts in general relativity
- All stub articles
- Relativity stubs
- Mathematical physics stubs