Physical interpretation of Kundt spacetimes using geodesic deviation

TL;DR

This paper analyzes Kundt spacetimes in higher dimensions using geodesic deviation, revealing how different algebraic types influence test particle motion and how these effects can be measured by gravitational detectors.

Contribution

It provides a comprehensive invariant-based analysis of geodesic deviation in all algebraically special Kundt spacetimes, linking algebraic classification to observable particle motions.

Findings

Different algebraic types produce distinct geodesic deviation patterns.

The invariant quantities classify the spacetime types and determine test particle behavior.

Gravitational wave effects depend on the algebraic subtype and background geometry.

Abstract

We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that the local effect of such gravitational fields on the particles basically consists of isotropic motion caused by the cosmological constant Lambda, Newtonian-type tidal deformations typical for spacetimes of algebraic type D or II, longitudinal motion characteristic for spacetimes of type III, and type N purely transverse effects of exact gravitational waves with D(D-3)/2 polarizations. We explicitly discuss the canonical forms of the geodesic deviation motion in all algebraically special subtypes of the Kundt family for which the optically privileged direction is a multiple Weyl aligned null direction (WAND), namely D(a), D(b), D(c), D(d), III(a), III(b), IIIi, IIi, II(a), II(b), II(c) and II(d). We demonstrate that the key invariant quantities determining these algebraic types and subtypes also directly determine the specific local motion of test particles, and are thus measurable by gravitational detectors. As an example, we analyze an interesting class of type N or II gravitational waves which propagate on backgrounds of type O or D, including Minkowski, Bertotti-Robinson, Nariai and Plebanski-Hacyan universes.