Dominant energy condition and causality for Skyrme-like generalizations of the wave-map equation

TL;DR

This paper demonstrates that a class of Skyrme-like field theories related to wave-maps satisfy the dominant energy condition, ensuring finite propagation speed, thus extending previous results in the field.

Contribution

It establishes the dominant energy condition for a broad class of Skyrme-like theories, generalizing recent findings and confirming causality properties.

Findings

The theories obey the dominant energy condition.

Finite speed of propagation is guaranteed by Hawking's theorem.

Generalizes previous results by Gibbons.

Abstract

It is shown in this note that a class of Lagrangian field theories closely related to the wave-map equation and the Skyrme model obeys the dominant energy condition, and hence by Hawking's theorem satisfies finite speed of propagation. The subject matter is a generalization of a recent result of Gibbons.