Speaker
Description
We present a rigorous proof establishing the mathematical equivalence between two independent criteria for the marginal stability of multi-fluid relativistic stars: the dynamical criterion based on the vanishing of the fundamental radial pulsation mode's eigenfrequency, and the static criterion derived from the geometric alignment of mass and particle number gradients in the parameter space. Leveraging this equivalence, we introduce a powerful and computationally efficient framework as an upgraded version of the critical curve method, to systematically map the stability boundaries for multi-fluid mixed stars across the entire parameter space of central pressures. Our analysis, applied to a variety of nuclear and dark matter equations of state, reveals the existence of stable region in the observable mass-radius diagram. By resolving degeneracies with 3-dimensional Mass-Radius-Pressure diagrams, we provide a complete topological view of the ensemble. This work supplies a robust theoretical foundation for interpreting multi-messenger astronomical observations and constraining the properties of dark matter.
