Algebraically special perturbations of the Schwarzschild solution in higher dimensions

TL;DR

This paper investigates algebraically special perturbations of higher-dimensional Schwarzschild solutions, revealing that only Myers-Perry deformations are regular, thus extending four-dimensional results and clarifying non-uniqueness issues in metric reconstruction.

Contribution

It generalizes known four-dimensional algebraically special perturbation results to higher dimensions, showing only Myers-Perry deformations are regular.

Findings

Only Myers-Perry deformations are regular algebraically special perturbations in higher dimensions.

Generalizes Couch and Newman's results to higher dimensions.

Clarifies the non-uniqueness in metric reconstruction from gauge-invariant variables.

Abstract

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".