Non-radial pulsations of gravitationally coupled two-fluid neutron stars in general relativity

TL;DR

This paper develops a fully relativistic framework for analyzing non-radial oscillations in two-fluid neutron stars, enabling better understanding of their structure and gravitational-wave signals.

Contribution

It introduces a novel formalism for polar perturbations of gravitationally coupled two-fluid neutron stars, including numerical methods for mode spectrum analysis.

Findings

Computed polar mode spectra for two-fluid neutron star models.

Classified fundamental and pressure modes by their dominant fluid character.

Established a basis for relativistic asteroseismology of multi-fluid stars.

Abstract

Non-radial oscillations of neutron stars provide a powerful probe of stellar structure and relativistic gravity, but a fully general relativistic treatment for gravitationally coupled two-fluid stars with independently conserved currents has so far been lacking. In this work, we develop a fully relativistic framework for polar perturbations of gravitationally coupled two-fluid neutron stars, assuming that the two fluids interact only through the common spacetime and are not coupled by entrainment or direct microphysical interactions. We derive the coupled linear perturbation equations governing the metric and both fluid components, and complete the formulation by establishing the regularity, surface, and exterior matching conditions required for a well-posed oscillation eigenvalue problem. We then implement the resulting system numerically and compute representative polar mode spectra for gravitationally coupled two-fluid stellar models. This implementation provides a practical way to address mode identification in gravitationally coupled two-fluid stars, allowing the fundamental ($\mathsf{f}$) and pressure ($\mathsf{p}$) mode branches of the spectrum to be classified according to their dominant inner- or outer-fluid character through the associated eigenfunctions and their node structure. The formalism developed here provides a foundation for extending relativistic asteroseismology to multi-fluid compact stars and for exploring their potential gravitational-wave signatures in a fully general relativistic setting.