Dynamics of Fast Rotating Neutron Stars: An Approach in the Hilbert Gauge

TL;DR

This paper presents a numerical framework for studying non-axisymmetric oscillations of rapidly rotating neutron stars in full General Relativity, incorporating dynamic spacetime effects and achieving high accuracy at low computational cost.

Contribution

It introduces a new set of evolution equations in the Hilbert gauge for non-axisymmetric perturbations of rotating neutron stars, with a stable and efficient numerical implementation.

Findings

Successfully extracted oscillation mode frequencies up to the Kepler limit.

Demonstrated high accuracy with low computational expense.

Validated the approach for dynamic spacetime contributions.

Abstract

We describe a set of time evolution equations and its numerical implementation for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full General Relativity, taking into account the contribution of a dynamic spacetime. We derive the perturbation equations for the spacetime in the Hilbert gauge, while the hydrodynamical evolution is based on perturbations of the energy-momentum tensor. In our numerical implementation, we use Kreiss-Oliger dissipation in order to achieve a stable time evolution. Our code features high accuracy at comparably low computational expense and we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit.