Kundt spacetimes in the Gauss-Bonnet Gravity

TL;DR

This paper investigates Kundt spacetimes within Gauss-Bonnet gravity, analyzing their geometric properties, field equations constraints, and algebraic types to understand their structure in this extended gravity theory.

Contribution

It provides a detailed analysis of Kundt solutions in Gauss-Bonnet gravity, including constraints from field equations and algebraic classification, which was not previously explored.

Findings

Kundt solutions without gyratonic terms are characterized in Gauss-Bonnet gravity.

Constraints on metrics depend on algebraic types and field equations.

Conditions for various algebraic types of Kundt spacetimes are established.

Abstract

The Gauss-Bonnet gravity is a special case of so-called Quadratic Gravity, which is an extension of Einstein's theory with additional terms in action that are quadratic combinations of the Riemann tensor and its contractions. These corrections are needed, for example, in perturbative quantum gravity. We consider the family of Kundt spacetimes, which is defined in a purely geometrical way by admitting a shear-free, twist-free and expansion-free null geodesic congruence. In particular, we focus on the Kundt solutions without gyratonic terms, and we investigate the constraints imposed by the Einstein-Gauss-Bonnet field equations. The conditions for the metrics to be of various algebraic types are also studied.