Locally Homogeneous Kundt Triples and CSI Metrics

Abstract

A pseudo-Riemannian manifold is called CSI if all scalar polynomial invariants constructed from the curvature tensor and its covariant derivatives are constant. In the Lorentzian case, the CSI spacetimes have been studied extensively due to their application to gravity theories. It is conjectured that a CSI spacetime is either locally homogeneous or belongs to the subclass of degenerate Kundt metrics. Independent of this conjecture, any CSI spacetime can be related to a particular locally homogeneous degenerate Kundt metric sharing the same scalar polynomial curvature invariants. In this paper we will invariantly classify the entire subclass of locally homogeneous CSI Kundt spacetimes which are of alignment type {\bf D} to all orders and show that any other CSI Kundt metric can be constructed from them.

17 pages

References in corpus (9)

• Type II universal spacetimes
• Pseudo-Riemannian VSI spaces II
• Universal electromagnetic fields
• Multiple Killing Horizons
• Universal spacetimes in four dimensions
• Vacuum Kundt Waves
• Chaotic motion in Kundt spacetimes
• Spacetimes foliated by non-expanding null surfaces in the presence of a cosmological constant
• $\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds

Cited by in corpus (2)

• Kundt Three Dimensional Left Invariant Spacetimes
• $\mathcal{I}$-Preserving Diffeomorphisms of Lorentzian Manifolds