  We study algebraically special perturbations of a generalized Schwarzschild
solution in any number of dimensions. There are two motivations. First, to
learn whether there exist interesting higher-dimensional algebraically special
solutions beyond the known ones. Second, algebraically special perturbations
present an obstruction to the unique reconstruction of general metric
perturbations from gauge-invariant variables analogous to the Teukolsky scalars
and it is desirable to know the extent of this non-uniqueness. In four
dimensions, our results generalize those of Couch and Newman, who found
infinite families of time-dependent algebraically special perturbations. In
higher dimensions, we find that the only regular algebraically special
perturbations are those corresponding to deformations within the Myers-Perry
family. Our results are relevant for several inequivalent definitions of
"algebraically special".
