Abstract
We present a comparative analysis of the self-gravitating solitons that arise in the Einstein–Klein–Gordon, Einstein–Dirac, and Einstein–Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study by Herdeiro, Pombo and Radu in 2017, the matter fields possess suitable self-interacting terms in the Lagrangians, which allow for the existence of Q-ball-type solutions for these models in the flat spacetime limit. In spite of this important difference, our analysis shows that the high degree of universality that was observed by Herdeiro, Pombo and Radu remains, and various spin-independent common patterns are observed.
Highlights
The latter, dubbed Skyrmions, exist in a model with four scalars that are subject to a constraint. They were proposed as field theory realizations of baryons; Skyrmions capture the basic properties of a generic soliton
A interesting case concerns the study of backreaction of these solutions on the spacetime geometry. This is a legitimate question, since the existence of solitons relies on the nonlinearity of the field theory and General Relativity (GR) is intrinsically highly nonlinear
The boundary conditions that are satisfied by the functions ψ at r = 0, ∞ are similar to those in the gravitating case, as given
Summary
One expects that a subset of solutions with M smaller than the mass of Q free particles (bosons or fermions) may be stable, which is possible along the lower frequency branch This case is likely physically less relevant (since the potential U is not positive definite); it possesses some interesting properties, which depend, to some extent, on the spin of the field. The pattern of Dirac solitons without a sextic self-interaction (which was the original case in the pioneering work by Soler [20] ) seems to be similar to the one that is found in the β > 0 case, see Figure 2 (right panel) Both M and Q still diverge at the limits of the w-interval
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