We study algebraically special perturbations of a generalized Schwarzschildsolution in any number of dimensions. There are two motivations. First, tolearn whether there exist interesting higher-dimensional algebraically specialsolutions beyond the known ones. Second, algebraically special perturbationspresent an obstruction to the unique reconstruction of general metricperturbations from gauge-invariant variables analogous to the Teukolsky scalarsand it is desirable to know the extent of this non-uniqueness. In fourdimensions, our results generalize those of Couch and Newman, who foundinfinite families of time-dependent algebraically special perturbations. Inhigher dimensions, we find that the only regular algebraically specialperturbations are those corresponding to deformations within the Myers-Perryfamily. Our results are relevant for several inequivalent definitions of"algebraically special".
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