General Kundt spacetimes in higher dimensions

TL;DR

This paper explores the geometry and curvature of higher-dimensional Kundt spacetimes, deriving Einstein-Maxwell equations and identifying key subclasses like pp-waves and gyratons, expanding understanding of these solutions in gravity theories.

Contribution

It provides a comprehensive analysis of higher-dimensional Kundt spacetimes, including curvature calculations, algebraic classifications, and explicit Einstein-Maxwell equations, with new subclasses and special cases identified.

Findings

Derived all curvature and Ricci tensor components for Kundt spacetimes.

Identified algebraic types and geometric constraints under Einstein's equations.

Characterized key subclasses such as generalized pp-waves, VSI, CSI, and gyratons.

Abstract

We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subclasses of the Kundt family and we identify the most important special cases, namely generalised pp-waves, VSI or CSI spacetimes, and gyratons.