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

Building upon the methods used recently in [1], 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 θ 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(θ) and g(θ) (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.