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

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 (Rezzolla L and Yoshida S 2001 Class. Quantum Grav. 18 L87) 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.