Impurity-doped stable domain walls in spherically symmetric spacetimes

Abstract

In this work, radially symmetric domain wall solutions in the presence of impurities are investigated for both flat and curved D+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D+1$$\\end{document} spacetimes, with geometry generated by a rotationally invariant background metric. We have examined the constraints placed upon the model by Derrick’s theorem, and found out the Bogomol’nyi bound and equations of the symmetric restriction to this theory. Impurity-doped versions of a ϕ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^4$$\\end{document} model in two dimensions and a model with logarithmic potential in a Schwarzschild background have been explicitly worked out. The resulting configurations have been compared with those found in the homogeneous version of the theory, so that the effect of impurities in the form of solutions may be better appreciated. We have also generalized to higher dimensions some of the results that had been presented in the recent literature. These results relate to the possibility of BPS-preserving impurities, which we have found to still exist in the spacetimes considered in this work. We also investigate ways in which these results may be extended in a curved background.