Non-topological soliton Bardeen boson stars and their frozen states

被引：0

作者：

Zhen-Hua Zhao ^{[1
]}

Yi-Ning Gu ^{[1
]}

Shu-Cong Liu ^{[2
]}

Long-Xing Huang ^{[2
]}

Yong-Qiang Wang ^{[2
]}

机构：

[1] Shandong University of Science and Technology,Department of Applied Physics

[2] Lanzhou University,School of Physical Science and Technology

来源：

The European Physical Journal C | / 85卷 / 5期

关键词：

D O I：

10.1140/epjc/s10052-025-14228-4

中图分类号：

学科分类号：

摘要：

We investigate a Bardeen model coupling Einstein gravity with nonlinear electromagnetic fields and non-topological soliton complex scalar fields, governed by the magnetic charge q~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}$$\end{document}, the complex scalar field frequency ω~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\omega }$$\end{document}, and the self-interaction parameter η~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\eta }$$\end{document}. Our results reveal that the magnetic charge q~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}$$\end{document} exhibits η~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\eta }$$\end{document}-dependent critical values q~c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}_c$$\end{document}, beyond which (q~>q~c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q} > \tilde{q}_c$$\end{document}) Bardeen boson stars (BBSs) may transition into frozen states (ω~→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\omega } \rightarrow 0$$\end{document}). These frozen states are characterized by a critical horizon whose radius r~cH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}^\textrm{H}_{c}$$\end{document} satisfies r~innerH,RN<r~c<r~outerH,RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}_{\text {inner}}^{\text {H,RN}}< \tilde{r}_{c} < \tilde{r}_{\text {outer}}^{\text {H,RN}}$$\end{document}, where r~innerH,RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}_{\text {inner}}^{\text {H,RN}}$$\end{document} and r~outerRN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}_{\text {outer}}^{\text {RN}}$$\end{document} denote the inner and outer horizons of magnetic Reissner–Nordström (RN) black holes with equivalent mass and magnetic charge. Notably, the ADM mass of frozen BBSs is independent of η~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\eta }$$\end{document}. Furthermore, light ring (LR) solutions exist universally across all tested combinations of q~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}$$\end{document} and η~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\eta }$$\end{document}, with all frozen BBSs exhibiting LRs whose outer radius r~outerLR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}_{\text {outer}}^{\text {LR}}$$\end{document} is independent of η~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\eta }$$\end{document}. Compared to magnetic RN black holes, frozen BBSs possess a smaller outer LR radius (r~outerLR<r~outerLR, RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{r}_{\text {outer}}^{\text {LR}} < \tilde{r}_{\text {outer}}^{\text {LR, RN}}$$\end{document}).

引用