Why Stellar Sequences Turn Over: Fixed Points, Instability, and Equation-of-State Universality
The paper reformulates stellar structure equations using dynamical systems to explain why stellar sequences have a maximum mass. It shows that this maximum mass occurs when a system reaches a fixed point in its relativistic regime, which corresponds to the turnover in the mass-radius curve. This fixed point implies an effective reduction in dimensionality near instability, leading to universal scaling relations independent of specific equation-of-state details.