Radial oscillations and stability of multiple-fluid compact stars

TL;DR

This paper develops a generalized framework for analyzing radial oscillations and stability in multi-fluid compact stars, extending Chandrasekhar's single-fluid pulsation equations to multiple fluids with gravitational interactions.

Contribution

It introduces a new set of pulsation equations for multi-fluid stars, allowing detailed stability analysis of complex stellar compositions.

Findings

Derived pulsation equations for multi-fluid stars.

Provided solutions for one-, two-, and three-fluid models.

Demonstrated the applicability of the equations to various stellar configurations.

Abstract

I derive a system of pulsation equations for compact stars made up of an arbitrary number of perfect fluids that can be used to study radial oscillations and stability with respect to small perturbations. I assume spherical symmetry and that the only inter-fluid interactions are gravitational. My derivation is in line with Chandrasekhar's original derivation for the pulsation equation of a single-fluid compact star and keeps the contributions from the individual fluids manifest. I illustrate solutions to the system of pulsations equations with one-, two-, and three-fluid examples.