21 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
Non-adiabatic radiative collapse of a relativistic star under different initial conditions
We examine the role of space-time geometry in the non-adiabatic collapse of a
star dissipating energy in the form of radial heat flow, studying its evolution
under different initial conditions. The collapse of a star with interior
comprising of a homogeneous perfect fluid is compared with that of a star
filled with inhomogeneous imperfect fluid with anisotropic pressure. Both the
configurations are spherically symmetric, however, in the latter case, the
physical space of the configurations is assumed to be
inhomogeneous endowed with spheroidal or pseudo-spheroidal geometry. It is
observed that as long as the collapse is shear-free, its evolution depends only
on the mass and size of the star at the onset of collapse.Comment: To appear in Pramana- j. of physic
Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
We give a model of the higher-dimensional spherically symmetric gravitational
collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation
of the basic equations is given for the spacetime with a perfect fluid and a cosmological constant. This is a
generalization of the Misner-Sharp formalism of the four-dimensional
spherically symmetric spacetime with a perfect fluid in general relativity. The
whole picture and the final fate of the gravitational collapse of a dust cloud
differ greatly between the cases with and . There are two
families of solutions, which we call plus-branch and the minus-branch
solutions. Bounce inevitably occurs in the plus-branch solution for ,
and consequently singularities cannot be formed. Since there is no trapped
surface in the plus-branch solution, the singularity formed in the case of
must be naked. In the minus-branch solution, naked singularities are
massless for , while massive naked singularities are possible for
. In the homogeneous collapse represented by the flat
Friedmann-Robertson-Walker solution, the singularity formed is spacelike for , while it is ingoing-null for . In the inhomogeneous collapse with
smooth initial data, the strong cosmic censorship hypothesis holds for and for depending on the parameters in the initial data, while a
naked singularity is always formed for . These naked
singularities can be globally naked when the initial surface radius of the dust
cloud is fine-tuned, and then the weak cosmic censorship hypothesis is
violated.Comment: 23 pages, 1 figure, final version to appear in Physical Review
Space-time inhomogeneity, anisotropy and gravitational collapse
We investigate the evolution of non-adiabatic collapse of a shear-free
spherically symmetric stellar configuration with anisotropic stresses
accompanied with radial heat flux. The collapse begins from a curvature
singularity with infinite mass and size on an inhomogeneous space-time
background. The collapse is found to proceed without formation of an even
horizon to singularity when the collapsing configuration radiates all its mass
energy. The impact of inhomogeneity on various parameters of the collapsing
stellar configuration is examined in some specific space-time backgrounds.Comment: To appear in Gen. Relativ. Gra