Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-08-23
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, TeX file, from a talk at GR16, Durban, South Africa, July, 2001
Scientific paper
HH-spaces, i.e., complex spacetimes, of Petrov type NxN are determined by a trio of pde's for two functions, lambda and a, of three independent variables (and also two gauge functions, chosen to be two of the independent variables if one prefers). As in common integrable systems, these form a second order, linear system for lambda; howver, here the integrability conditions, involving a, are more complicated than is common. Therefore, with the hope of finding new solutions, these equations are now constrained to also admit both one and two homothetic or Killing vectors. The case with one Killing and one homothetic vector reduces these equations to two ode's for two unknown functions of the one remaining variable. In addition, we also describe in detail the explicit forms of the metric, tetrad, connections, and curvature for twisting HH-spaces of Petrov type NxN, modulo the determining equations. This simplifies considerably the process of obtaining these details cleanly from earlier articles on the subject, thus simplifying access to the research area.
No associations
LandOfFree
Equations for Complex-Valued, Twisting, Type N, Vacuum Solutions, with one or two Killing/homothetic vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Equations for Complex-Valued, Twisting, Type N, Vacuum Solutions, with one or two Killing/homothetic vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equations for Complex-Valued, Twisting, Type N, Vacuum Solutions, with one or two Killing/homothetic vectors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-189953