Relativistic Stellar Pulsations With Near-Zone Boundary Conditions

TL;DR

This paper introduces a new approximation method for calculating relativistic stellar pulsation modes by applying near-zone boundary conditions, simplifying computations while maintaining high accuracy in frequency predictions.

Contribution

It presents a novel approach that imposes boundary conditions at the star's surface, reducing complexity and improving frequency prediction accuracy for relativistic stellar models.

Findings

Frequency predictions are accurate to better than 0.01% for most models.

The method accurately predicts the real parts of pulsation frequencies.

Imprecision in imaginary parts is about M/R, the star's compactness ratio.

Abstract

A new method is presented here for evaluating approximately the pulsation modes of relativistic stellar models. This approximation relies on the fact that gravitational radiation influences these modes only on timescales that are much longer than the basic hydrodynamic timescale of the system. This makes it possible to impose the boundary conditions on the gravitational potentials at the surface of the star rather than in the asymptotic wave zone of the gravitational field. This approximation is tested here by predicting the frequencies of the outgoing non-radial hydrodynamic modes of non-rotating stars. The real parts of the frequencies are determined with an accuracy that is better than our knowledge of the exact frequencies (about 0.01%) except in the most relativistic models where it decreases to about 0.1%. The imaginary parts of the frequencies are determined with an accuracy of approximately M/R, where M is the mass and R is the radius of the star in question.