Dynamical stability of the two-fluid configurations

Determine the dynamical stability boundary of the analytically constructed two-fluid relativistic star by analyzing its coupled radial perturbation equations and the squared frequency of its fundamental radial mode, and compare that boundary with the Buchdahl-like critical compactness obtained from the divergence of the central pressure.

Background

The paper derives a family of static configurations consisting of a mixed ordinary-matter–dark-matter incompressible core and an ordinary-matter envelope. Its critical curve is defined by divergence of the central pressure and is explicitly distinguished from a dynamical stability threshold.

The authors note that stability in relativistic two-perfect-fluid systems requires solving the coupled radial perturbation equations and examining the fundamental mode. Applying this analysis would establish whether configurations inside the statically admissible region are dynamically stable and would permit a direct comparison between the true stability boundary and the paper’s Buchdahl-like critical curve.

References

The present analysis concerns the existence and static physical admissibility of the configurations and does not establish their dynamical stability. In particular, the critical curve obtained from the divergence of the central pressure defines a Buchdahl-like critical compactness within the present construction, rather than a marginal-stability curve. This distinction is especially relevant for two-fluid relativistic stars. As shown in , radial stability in systems composed of two perfect fluids requires the analysis of the coupled radial perturbation equations, with stability determined by the sign of the squared frequency of the fundamental radial mode. Consequently, configurations lying within the physically admissible region identified here are not necessarily dynamically stable. A radial-mode analysis of the present analytical configurations would therefore provide a natural extension of this work and would allow the stability boundary to be compared directly with the critical compactness obtained here.

— An Analytical Two Incompressible Fluid Star with a Mixed Ordinary Dark Matter Core and an Ordinary Matter Envelope  (2608.20185 - Estrada et al., 20 Aug 2026) in Section 'M–R diagram'; Section 'Conclusions'