Generalizations of pp-wave spacetimes in higher dimensions

TL;DR

This paper explores higher-dimensional Lorentzian spacetimes where all scalar invariants from the Riemann tensor and derivatives vanish, extending the concept of pp-wave spacetimes relevant in string theory contexts.

Contribution

It introduces a class of higher-dimensional Lorentzian spacetimes with zero scalar invariants, generalizing known pp-wave solutions in the context of string theory.

Findings

Characterization of higher-dimensional spacetimes with vanishing scalar invariants

Extension of pp-wave spacetimes to higher dimensions

Relevance to string theory in curved backgrounds

Abstract

We shall investigate $D$-dimensional Lorentzian spacetimes in which all of the scalar invariants constructed from the Riemann tensor and its covariant derivatives are zero. These spacetimes are higher-dimensional generalizations of $D$-dimensional pp-wave spacetimes, which have been of interest recently in the context of string theory in curved backgrounds in higher dimensions.