Self-gravitating Higgs field of an asymmetric binary scalar charge

Abstract

The self-gravitating Higgs field of a scalar charge is studied in the case of an asymmetric scalar doublet containing not only the canonical but also a phantom component. We show that in the zeroth and first approximation in the smallness of the canonical and phantom scalar charges, the gravitational field of the scalar charge is described by the Schwarzschild–de Sitter metric with a cosmological constant determined by a stable equilibrium point — the vacuum potential of the canonical Higgs field and the zero value of the scalar potential. An equation for the perturbation of the stable value of the potential is obtained and studied, and the asymptotic behavior in the near and far zones is found. The averaging of microscopic oscillations of the scalar field is carried out and it is shown that the sign of the contribution of microscopic oscillations to the macroscopic energy of the scalar field is completely determined by the values of the fundamental constants of the Higgs potential of the asymmetric scalar doublet. Particular attention is paid to the case where the contribution of oscillations to the macroscopic energy and pressure densities is strictly equal to zero. Possible applications of the obtained solutions are discussed.