Spacetimes characterized by their scalar curvature invariants

Details Spacetimes characterized by their scalar curvature invariants Spacetimes characterized by their scalar curvature invariants

2009-01-07

arxiv.org/abs/0901.0791v2

Class.Quant.Grav.26:025013,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

38pages; v2: some corrections + refs

Scientific paper

10.1088/0264-9381/26/2/025013

In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce the notion of an $\mathcal{I}$-non-degenerate spacetime metric, which implies that the spacetime metric is locally determined by its curvature invariants. By determining an appropriate set of projection operators from the Riemann tensor and its covariant derivatives, we are able to prove a number of results (both in the algebraically general and in algebraically special cases) of when a spacetime metric is $\mathcal{I}$-non-degenerate. This enables us to prove our main theorem that a spacetime metric is either $\mathcal{I}$-non-degenerate or a Kundt metric. Therefore, a metric that is not characterized by its curvature invariants must be of degenerate Kundt form. We then discuss the inverse question of what properties of the underlying spacetime can be determined from a given a set of scalar polynomial invariants, and some partial results are presented. We also discuss the notions of \emph{strong} and \emph{weak} non-degeneracy.

Affiliated with

Also associated with

No associations

Rating

Spacetimes characterized by their scalar curvature invariants 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 Spacetimes characterized by their scalar curvature invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spacetimes characterized by their scalar curvature invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-720333