Second-order symmetric Lorentzian manifolds II: structure and global properties

TL;DR

This paper summarizes recent findings on the structure and global properties of second-order symmetric Lorentzian manifolds, revealing they are mainly a subclass of plane wave spacetimes, with implications for understanding their geometric and physical characteristics.

Contribution

It provides an explicit local form and global analysis of second-order symmetric Lorentzian manifolds, identifying them as a specific subclass of plane waves.

Findings

Second-order symmetric Lorentzian manifolds are essentially a subclass of plane waves.

Explicit local forms of these manifolds are characterized.

Global properties of these manifolds are summarized.

Abstract

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.