The motion of a spherical dust cloud is described by the
Lemaitre-Tolman-Bondi solution and is completely specified by initial values of
distributions of the rest mass density and specific energy of the dust fluid.
From generic initial conditions of this spherically symmetric collapse, there
appears a naked singularity at the symmetric center in the course of the
gravitational collapse of the dust cloud. So this might be a counter example to
the cosmic censorship hypothesis. To investigate the genericity of this
example, we examine the stability of the `nakedness' of this singularity
against odd-parity modes of non-spherical linear perturbations for the metric,
i.e., linear gravitational waves. We find that the perturbations do not diverge
but are well-behaved even in the neighborhood of the central naked singularity.
This means that the naked singularity formation process is marginally stable
against the odd-parity modes of linear gravitational waves.Comment: 19 pages, 12 figures, to be published in Physical Review
