Mass and topology of hypersurfaces in static perfect fluid spaces

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 \(\{f=c\}\) (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 \(\{f=c\}\) 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).