42 research outputs found
Stability of Naked Singularity arising in gravitational collapse of Type I matter fields
Considering gravitational collapse of Type I matter fields, we prove that,
given an arbitrary - mass function and a -
function (through the corresponding - metric function
), there exist infinitely many choices of energy distribution
function such that the `true' initial data () leads
the collapse to the formation of naked singularity. We further prove that the
occurrence of such a naked singularity is stable with respect to small changes
in the initial data. We remark that though the initial data leading to both
black hole and naked singularity form a "big" subset of the true initial data
set, their occurrence is not generic. The terms `stability' and `genericity'
are appropriately defined following the theory of dynamical systems. The
particular case of radial pressure has been illustrated in details
to get clear picture of how naked singularity is formed and how, it is stable
with respect to initial data.Comment: 16 pages, no figure, Latex, submitted to Praman