Equivalence of Stability Criteria for Multi-Fluid Stars

TL;DR

This paper proves the mathematical equivalence of two stability criteria for multi-fluid relativistic stars and introduces an efficient framework to map their stability boundaries, aiding interpretation of astronomical observations.

Contribution

It establishes the equivalence between dynamical and static stability criteria and develops a new computational method for stability analysis of multi-fluid stars.

Findings

Existence of stable regions in the mass-radius diagram.

Framework applicable to various nuclear and dark matter equations of state.

Complete topological mapping of stability boundaries.

Abstract

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.