On the r-mode spectrum of relativistic stars

TL;DR

This paper rigorously proves that the r-mode spectrum of relativistic stars includes a continuous part, confirming earlier theoretical predictions and providing a precise mathematical framework for understanding these oscillations.

Contribution

The paper offers a rigorous mathematical proof of the continuous component in the r-mode spectrum of relativistic stars, clarifying the spectral properties and verifying prior results.

Findings

The r-mode spectrum has a continuous part.

The spectrum is defined via a continuous linear operator.

The results confirm earlier theoretical predictions.

Abstract

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima (1998) about the nature of the r-mode spectrum.