Spacetime modes of relativistic stars

TL;DR

This paper investigates relativistic star pulsations using an approximation that neglects fluid motions, revealing the existence of pure spacetime modes and highlighting the role of general relativity in stellar oscillations.

Contribution

It introduces the Inverse Cowling Approximation for studying relativistic stellar pulsations and demonstrates the existence of pure spacetime modes independent of fluid motions.

Findings

The ICA spectrum resembles the full $w$-mode spectrum for highly damped oscillations.

Pure spacetime modes exist that do not depend on fluid motions.

The spectrum of superdense stars is similar to axial modes, emphasizing relativistic effects.

Abstract

The problem of relativistic stellar pulsations is studied in a somewhat ad hoc approximation that ignores all fluid motions. This {\em Inverse Cowling Approximation} (ICA) is motivated by two observations: 1) For highly damped ($w$-mode) oscillations the fluid plays very little role. 2) If the fluid motion is neglected the problem for polar oscillation modes becomes similar to that for axial modes. Using the ICA we find a polar mode spectrum that has all features of the $w$-mode spectrum of the full problem. Moreover, in the limit of superdense stars, we find the ICA spectrum to be qualitatively similar to that of the axial modes. These results clearly show the importance of general relativity for the pulsation modes of compact stars, and that there are modes whose existence do not depend on motions of the fluid at all; pure ``spacetime'' modes.