Constructing stellar objects with multiple necks

TL;DR

This paper explores the theoretical construction of perfect fluid stellar models with multiple necks in their optical geometry, demonstrating the existence of arbitrarily many and the effects of phase transitions using a dynamical systems approach.

Contribution

It introduces a generalized dynamical systems framework for modeling stellar objects with complex optical geometries, including phase transitions and multiple necks.

Findings

Existence of models with arbitrarily many necks

Phase transitions can produce secondary double necks

Generalized equations of state are compatible with multiple neck structures

Abstract

We discuss the construction of perfect fluid stellar objects having optical geometries with multiple necks corresponding to spatially closed unstable lightlike geodesics. We prove that there exist physically reasonable models with arbitrarily many necks. We also show how a first order phase transition can give rise to quite pronounced secondary double necks. The analysis is carried out using a modification of a recent dynamical systems formulation of the TOV equations due to Nilsson and Uggla. Our reformulation allows for a very general family of equations of state including, for example, phase transitions.