Abstract:
In this work, we analyze the stability of spherically symmetric spacetimes
sourced by perfect and anisotropic uids under a class of gravitational per-
turbations. This has been done in a gauge-invariant formalism developed by
Ishibashi and Kodama, where the perturbation equations are written in terms
of manifestly gauge-invariant variables. We study axial perturbations of such
spacetimes. The perturbation equations reduce to a single master equation
and the equations for conservation of the energy momentum tensor. As is
well-known, axial perturbations do not excite the uid perturbations when
the source is a perfect uid. We review this result and then show that when
the uid is anisotropic, this is still true provided the vector de ning the di-
rection of anisotropy is constant under the perturbation. Finally we conclude
by taking a speci c example of a spacetime sourced by an anisotropic uid
and analyzing the axial perturbations of this spacetime.
