Axion electrodynamics: Energy-momentum tensor, and possibilities for experimental tests

TL;DR

This paper explores the energy-momentum tensor in axion electrodynamics, discusses its experimental detectability, and presents specific scenarios including static forces in media and astrophysical axion signals.

Contribution

It provides a detailed analysis of the energy-momentum tensor in axion electrodynamics and proposes experimental tests for detecting axion-induced forces and signals.

Findings

Derived the energy-momentum tensor for axion electrodynamics in media.

Calculated axion-generated forces in a static uniform material.

Estimated the 'axion echo' signal from astrophysical axion clouds.

Abstract

Axion electrodynamics is based upon the Lagrangian of the electromagnetic (EM) field plus its interaction with the axions, and is accordingly a physically open system. It means that the four-divergence of the EM energy-momentum tensor is different from zero, implying in turn that the total EM energy and momentum (when integrated over all space) do not constitute a four-vector. The EM force is in principle accessible to experimental detection, just analogous to what is the case in ordinary electrodynamics. In the first half of this paper the energy-momentum aspects of axion electrodynamics are worked out in general, when the surroundings are allowed to be a medium with constant permittivity and permeability. In the second half, two examples are discussed. The first is a static situation, where a block of uniform material containing axions is exposed to external strong electric and magnetic fields. Assuming the axion amplitude $a(x)$ (i.e. its density) to increase linearly in one direction, we calculate the axion-generated forces. As a second example, we consider axions varying not with position but instead harmonically with time; this is the constellation usually assumed in astrophysics. Assuming a Gaussian profile for the EM wave emitted from the Earth towards an axion cloud in outer space, we make a calculation of the 'axion echo', the return signal.