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Comment on ‘Covariant perturbations of Schwarzschild black holes’

We present a modification to the results presented in Clarkson and Barrett (2003 Class. Quantum Grav. 20 3855–84) arising from a correction to the tensor commutation relations. We present the full tensor commutation relation for angular derivatives as applicable to locally rotationally symmetric class-II spacetimes before discussing the implications on the Schwarzschild result. As the results were derived in the harmonic domain, the analysis and results of Clarkson and Barrett (2003) are stable against the changes we present here with the changes occurring to the covariant wave equation for our dimensionless, gauge-invariant, frame-invariant, transverse-traceless tensor and not to the harmonically defined wave equation.