Harmonic and Wave Maps Coupled with Einstein's gravitation

TL;DR

This paper explores the coupled dynamics of harmonic and wave maps with Einstein's gravity, focusing on energy conditions and specific mappings from warped and wave-like Lorentzian manifolds.

Contribution

It introduces new results on energy conditions and properties of harmonic and wave maps within the context of Einstein's gravitational field.

Findings

Energy conditions for wave maps established

Harmonic maps from warped product manifolds analyzed

Wave maps from wave-like Lorentzian manifolds studied

Abstract

In this paper we discuss the coupled dynamics, following from a suitable Lagrangian, of a harmonic or wave map $\phi$ and Einstein's gravitation described by a metric $g$. The main results concern energy conditions for wave maps, harmonic maps from warped product manifolds, and wave maps from wave-like Lorentzian manifolds.