Lovelock vacua with a recurrent null vector field

TL;DR

This paper explores vacuum solutions in Lovelock gravity with a recurrent null vector field, analyzing their properties, special cases, and explicit solutions in various dimensions, revealing new classes of gravitational wave solutions.

Contribution

It provides a detailed analysis of Lovelock vacua with recurrent null vectors, including explicit solutions and conditions for arbitrary functions, expanding understanding of non-expanding gravitational waves in higher dimensions.

Findings

Solutions include non-expanding gravitational waves in Nariai-like backgrounds

Special cases allow arbitrary functions in solutions for certain coupling constants

Identifies classes of solutions satisfying all field equations for degenerate vacua

Abstract

Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a "generic" base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the pp-waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions $n=5,6$ as well as for particular choices of the base manifold. The obtained solutions describe various classes of non-expanding gravitational waves propagating, e.g., in Nariai-like backgrounds $M_2\times\Sigma_{n-2}$. An appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N, and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.