Abstract
We consider the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity in four spacetime dimensions. The renormalizable Friedberg-Lee-Sirlin model consists of two interacting scalar fields, where the mass of the complex scalar field results from the interaction with the real scalar field which has a finite vacuum expectation value. We here study a new family of self-gravitating axially-symmetric, rotating boson stars in this model. In the flat space limit these boson stars tend to the corresponding Q-balls. Subject to the usual synchronization condition, the model admits spinning hairy black hole solutions with two different types of scalar hair. We here investigate parity-even and parity-odd boson stars and their associated hairy black holes. We explore the domain of existence of the solutions and address some of their physical properties. The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit.
Highlights
The solutions exhibit close similarity to the corresponding boson stars and Kerr black holes with synchronised scalar hair in the O(3)-sigma model coupled to Einstein gravity and to the corresponding solutions in the Einstein-Klein-Gordon theory with a complex scalar field, where the latter are recovered in a limit
All these self-gravitating configurations exist for a certain range of values of the parameters of the respective theory, For instance, there are two branches of self-gravitating Skyrmions [4, 5], where the lower in energy branch is linked to the flat space Skyrmion in the limit of a vanishing effective gravitational coupling
We extend the study of the spinning boson stars and hairy black holes, by constructing new families of stationary rotating solutions in the Friedberg-Lee-Sirlin model minimally coupled to Einstein gravity
Summary
It follows from the linearized field equations (2.7) that the parameters μ and m determine the mass of the real and complex scalar fields, respectively. The flat-space localized regular solutions of the Friedberg-Lee-Sirlin model (2.2) exist in the limit of vanishing scalar potential, μ → 0, when the vacuum expectation value of the real component ψ is kept non-zero [64, 65]. They represent Q-balls with a long-range massless scalar component. There are families of corresponding boson stars and hairy black holes with synchronised hair in the complex-Klein-Gordon field theory minimally coupled to Einstein’s gravity [24, 46, 48, 61, 63]
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