Mass and topology of hypersurfaces in static perfect fluid spacesMass and topology of hypersurfaces in static perfect fluid spacesM. Andrade et al.

We investigate the topological implications of stable minimal surfaces existing in a static perfect fluid space while ensuring that the fluid satisfies certain energy conditions. Based on the main findings, the topology of the level set {f=c}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{f=c\}$$\end{document} (the boundary of a stellar model) is studied, where c is a positive constant and f is the static potential of a static perfect fluid space. Bounds for the Hawking mass for the level set {f=c}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{f=c\}$$\end{document} of a static perfect fluid space are derived. Consequently, we prove an inequality that resembles the Penrose inequality for compact and non-compact static perfect fluid spaces, guaranteeing that the Hawking mass is positive for a class of surfaces in a static perfect fluid space. We will present a section dedicated to examples of static stellar models, one of them inspired by Witten’s black hole (or Hamilton’s cigar).