Differential invariants of Kundt waves

Abstract

Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt waves. The results are then compared to the invariants computed by the Cartan-Karlhede algorithm.

Differential invariants of Kundt spacetimes

“…Consider the action of G (1) 0 on the fiber π −1 1,0 (p 0 ) ∩ E 1 . Here W 2 v is an absolute invariant, with the action transitive on its level sets 16 . As shown in section 3.2, we can bring any point to the point (omitting equations of p 0 )…”

“…Several subclasses of Kundt metrics have been discussed in the literature using the Cartan-Karlhede algorithm, see [21] and references therein. For Kundt waves in 4D we compared both approaches, via sdi and cci, in [16]. In the present paper we discuss the general situation in general dimension n, with special attention given to dimensions 3 and 4.…”

Killing tensors in Koutras–Mcintosh spacetimes

“…They belong to a more general class of spacetimes not separated by their scalar curvature invariants [4,5], which in dimension 4 were proven to be of degenerate Kundt type. Note that Kundt spaces can be distinguished by their Cartan [19] or differential [16] invariants, see [15] for a comparison.…”