Boson Stars and Boson Shells

In this work we present a broad formalism for a study of the models of black holes, boson stars, boson shells and wormholes. The studies of boson stars and boson shells in a theory involving Scalar field, U(1) gauge field and a shelf interacting scalar potential coupled to gravity in the presence of a cosmological constant Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document} are presented in details.