Equivalence of Stability Criteria for Multi-Fluid Stars

Equivalence of Stability Criteria for Multi-Fluid Stars
Tian-Shun Chen, Xiao-Ding Zhou, Hao Feng, Kilar Zhang
arXiv:2512.01640v2 Announce Type: replace
Abstract: We prove a static criterion for radial zero modes in relativistic multi-fluid stars whose isentropic barotropic components are separately conserved and interact only through gravity. For a regular multi-parameter equilibrium family, the particle-number map is rank deficient if and only if a nontrivial physical radial zero mode exists. The proof establishes a one-to-one correspondence between particle-preserving infinitesimal equilibrium deformations and zero-frequency radial perturbations. We also construct the self-adjoint form realization associated with the coupled pulsation operator, prove that it has compact resolvent, show that its eigenspaces coincide with the physical radial-mode spaces, and establish continuity of every ordered squared mode frequency along the equilibrium family. It follows that every boundary point of strict radial stability within the equilibrium family satisfies the static rank condition. A representative two-fluid example shows that the static criterion and the dynamical zero-mode calculation yield the same critical curve. The rank condition therefore provides an equilibrium-based method for locating radial zero modes and determining their multiplicity.arXiv:2512.01640v2 Announce Type: replace
Abstract: We prove a static criterion for radial zero modes in relativistic multi-fluid stars whose isentropic barotropic components are separately conserved and interact only through gravity. For a regular multi-parameter equilibrium family, the particle-number map is rank deficient if and only if a nontrivial physical radial zero mode exists. The proof establishes a one-to-one correspondence between particle-preserving infinitesimal equilibrium deformations and zero-frequency radial perturbations. We also construct the self-adjoint form realization associated with the coupled pulsation operator, prove that it has compact resolvent, show that its eigenspaces coincide with the physical radial-mode spaces, and establish continuity of every ordered squared mode frequency along the equilibrium family. It follows that every boundary point of strict radial stability within the equilibrium family satisfies the static rank condition. A representative two-fluid example shows that the static criterion and the dynamical zero-mode calculation yield the same critical curve. The rank condition therefore provides an equilibrium-based method for locating radial zero modes and determining their multiplicity.