General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

TL;DR

This paper demonstrates that the first-order general relativistic description of Rossby-Haurwitz waves on a rotating fluid shell can be derived from the Newtonian case via coordinate transformation, extending previous Newtonian results to GR.

Contribution

It shows that Newtonian Rossby-Haurwitz wave results are applicable in general relativity at first order in angular velocity through a coordinate transformation.

Findings

GR Rossby-Haurwitz waves can be obtained from Newtonian ones at first order.

Newtonian results by Rezzolla and Yoshida are valid in GR at first order.

The approach simplifies GR analysis of waves on rotating shells.

Abstract

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.