On the inexistence of self-gravitating solitons in generalised axion electrodynamics

TL;DR

This paper proves that self-gravitating solitonic solutions do not exist in a generalized axion electrodynamics model, including static and stationary spacetimes, extending previous results to more general couplings.

Contribution

It establishes the nonexistence of self-gravitating axionic solitons in a broad class of Einstein-Maxwell-axion models, even with non-minimal couplings and relaxed symmetry assumptions.

Findings

No static axionic solitons in the model.

No stationary axionic solitons under mild assumptions.

Results hold for generic couplings $f( heta)$ and $g( heta)$.

Abstract

Building upon the methods used recently, we establish the inexistence of self-gravitating solitonic solutions for both static and strictly stationary asymptotically flat spacetimes in generalised axion electrodynamics. This is an Einstein-Maxwell-axion model, where the axion field $\theta$ is non-minimally coupled to the electromagnetic field. Considering the standard QCD axion coupling, we first present an argument for the absence of static axionic solitons, $i.e.$ localised energy axionic-electromagnetic configurations, yielding an everywhere regular, horizonless, asymptotically flat, static spacetime. Then, for generic couplings $f(\theta)$ and $g(\theta)$ (subject to mild assumptions) between the axion field and the electromagnetic field invariants, we show there are still no solitonic solutions, even when dropping the staticity assumption and merely requiring a strictly stationary spacetime, regardless of the spatial isometries.