Covariant approach for perturbations of rotationally symmetric spacetimes

We present a covariant decomposition of Einstein’s field equations which is particularly suitable for perturbations of spherically symmetric—and general locally rotationally symmetric—spacetimes. Based upon the utility of the $1+3$ covariant approach to perturbation theory in cosmology, the semi-tetrad, $1+1+2$ approach presented here should be useful for analyzing perturbations of a variety of systems in a covariant and gauge-invariant manner. Such applications range from stellar objects to cosmological models such as the spherically symmetric Lemaître-Tolman-Bondi solutions or the class of locally rotationally symmetric Bianchi models.