Nonradial oscillations of realistic anisotropic neutron stars: Polar modes
Abstract
In this work, we study the polar perturbations of static, spherically symmetric neutron stars with anisotropic pressure in full general relativity, including linear-order perturbations of both the metric and the fluid. We calculate the f-mode frequencies and the corresponding damping times using a consistent treatment of the perturbation of the radial vector kα. In particular, its Lagrangian perturbation Δkα is determined by the metric perturbations and the fluid Lagrangian displacement and is constrained to the (ũ,k̃) plane, where ũα is the normalized fluid four-velocity. This constraint introduces an additional dynamical degree of freedom into the perturbation equations. Considering three equations of state and the Horvat and Bowers-Liang prescriptions for pressure anisotropy, we find that the f-mode frequency increases with stellar mass, ranging from $1$ to $3$~kHz, while the damping time decreases, ranging from $0.5$ to $1.25$~s. Increasing anisotropy, in the sense of tangential pressure exceeding radial pressure, generally lowers the oscillation frequency, while its effect on the damping time depends on the anisotropy prescription: the damping time decreases with increasing anisotropy for the Horvat model but increases with increasing anisotropy for the Bowers-Liang model. We further find quasi-universal relations between the real and imaginary parts of the f-mode frequency, MωR and MωI, and the stellar compactness 𝒞=M/R, which are largely insensitive to the equation of state. Polynomial fits to these relations achieve an accuracy better than 10%, providing a simple phenomenological framework for constraining neutron-star pressure anisotropy through future asteroseismology observations.
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BibTeX
@misc{becerra2026nonradial,
title = {{Nonradial oscillations of realistic anisotropic neutron stars: Polar modes}},
author = {L. M. Becerra and José F. Rodríguez-Ruiz and E. A. Becerra-Vergara and F. D. Lora-Clavijo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07878},
eprint = {2609.07878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07878},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonradial oscillations of realistic anisotropic neutron stars: Polar modes
AU - L. M. Becerra
AU - José F. Rodríguez-Ruiz
AU - E. A. Becerra-Vergara
AU - F. D. Lora-Clavijo
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07878
UR - https://arxiv.org/abs/2609.07878
AB - In this work, we study the polar perturbations of static, spherically symmetric neutron stars with anisotropic pressure in full general relativity, including linear-order perturbations of both the metric and the fluid. We calculate the f-mode frequencies and the corresponding damping times using a consistent treatment of the perturbation of the radial vector k^α. In particular, its Lagrangian perturbation Δk^α is determined by the metric perturbations and the fluid Lagrangian displacement and is constrained to the (ũ,k̃) plane, where ũ^α is the normalized fluid four-velocity. This constraint introduces an additional dynamical degree of freedom into the perturbation equations. Considering three equations of state and the Horvat and Bowers-Liang prescriptions for pressure anisotropy, we find that the f-mode frequency increases with stellar mass, ranging from $1$ to $3$~kHz, while the damping time decreases, ranging from $0.5$ to $1.25$~s. Increasing anisotropy, in the sense of tangential pressure exceeding radial pressure, generally lowers the oscillation frequency, while its effect on the damping time depends on the anisotropy prescription: the damping time decreases with increasing anisotropy for the Horvat model but increases with increasing anisotropy for the Bowers-Liang model. We further find quasi-universal relations between the real and imaginary parts of the f-mode frequency, Mω_R and Mω_I, and the stellar compactness 𝒞=M/R, which are largely insensitive to the equation of state. Polynomial fits to these relations achieve an accuracy better than 10%, providing a simple phenomenological framework for constraining neutron-star pressure anisotropy through future asteroseismology observations.
ER -