The Riemann tensor, the metric tensor, and curvature collineations in general relativity
Copyright policy )The Riemann tensor, the metric tensor, and curvature collineations in general relativity
The equation xμνRμ λαβ+xμλRμ ναβ = 0, where xμν and Rμ ναβ are the components of an arbitrary symmetric tensor and of the Riemann tensor formed from the metric tensor gμν, is trivially satisfied by xμν = φgμν. Nontrivial solutions are important in various areas of general relativity such as in the study of curvature collineations, and also in the study of algebraic methods given by Hlavatý and Ihrig for the determination of gμν, from a given set of Rμ ναβ. We have found all Rμ ναβ for which there exist nontrivial solutions of the above equation, and we have given the form of the xμν in each case. Various examples of space–times for explicit nontrivial solutions are discussed.
- Monash University Australia
- Massey University New Zealand
Local differential geometry of Lorentz metrics, indefinite metrics, curvature collineations, Riemann tensor, spacetimes
Local differential geometry of Lorentz metrics, indefinite metrics, curvature collineations, Riemann tensor, spacetimes
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).20 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!