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arXiv · 1301.7068

Algebraically special perturbations of the Schwarzschild solution in higher dimensions

Oscar J. C. Dias·Harvey S. Reall
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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".

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Oscar J. C. Dias, Harvey S. Reall. 2013-01-29. Algebraically special perturbations of the Schwarzschild solution in higher dimensions. https://doi.org/10.1088/0264-9381/30/9/095003

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