GRAVITATIONAL-WAVES AROUND A NAKED SINGULARITY - ODD-PARITY PERTURBATION OF LEMAITRE-TOLMAN-BONDI SPACE-TIME

The motion of a spherical dust cloud is described by the Lemaitre-Tolm an-Bondi solution and is completely specified by initial values of dis tributions of the rest mass density and specific energy of the dust fl uid. From generic initial conditions of this spherically symmetric col lapse, there appears a naked singularity at the symmetric center in th e course of the gravitational collapse of the dust cloud. So this migh t be a counterexample to the cosmic censorship hypothesis. To investig ate the genericity of this example, we examine the stability of the '' nakedness'' of this singularity against odd-parity modes of non-spheri cal linear perturbations for the metric, i.e., linear gravitational wa ves. We find that the perturbations do not diverge but are well-behave d even in the neighborhood of the central naked singularity. This mean s that the naked singularity formation process is marginally stable ag ainst the odd-parity modes of linear gravitational waves.