446,354 research outputs found
Curvature conditions for the occurrence of a class of spacetime singularities
It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that
a generic gravitational collapse cannot result in a naked singularity
accompanied by closed timelike curves. An important role in this result plays
the so-called inextendibility condition, which is required to hold for certain
incomplete null geodesics. In this paper, a theorem is proved that establishes
some relations between the inextendibility condition and the rate of growth of
the Ricci curvature along incomplete null geodesics. This theorem shows that
the inextendibility condition may hold for a much more general class of
singularities than only those of the strong curvature type. It is also argued
that some earlier cosmic censorship results obtained for strong curvature
singularities can be extended to singularities corresponding to the
inextendibility condition.Comment: RevTeX, 6 pages, no figures. To be published in J. Math. Phy
Can we see naked singularities?
We study singularities which can form in a spherically symmetric
gravitational collapse of a general matter field obeying weak energy condition.
We show that no energy can reach an outside observer from a null naked
singularity. That means they will not be a serious threat to the Cosmic
Censorship Conjecture (CCC). For the timelike naked singularities, where only
the central shell gets singular, the redshift is always finite and they can in
principle, carry energy to a faraway observer. Hence for proving or disproving
CCC the study of timelike naked singularities will be more important. Our
results are very general and are independent of initial data and the form of
the matter.Comment: 10 page
Spherical gravitational collapse in N-dimensions
We investigate here spherically symmetric gravitational collapse in a
spacetime with an arbitrary number of dimensions and with a general {\it type
I} matter field, which is a broad class that includes most of the physically
reasonable matter forms. We show that given the initial data for matter in
terms of the initial density and pressure profiles at an initial surface
from which the collapse evolves, there exist rest of the initial data
functions and classes of solutions of Einstein equations which we construct
here, such that the spacetime evolution goes to a final state which is either a
black hole or a naked singularity, depending on the nature of initial data and
evolutions chosen, and subject to validity of the weak energy condition. The
results are discussed and analyzed in the light of the cosmic censorship
hypothesis in black hole physics. The formalism here combines the earlier
results on gravitational collapse in four dimensions in a unified treatment.
Also the earlier work is generalized to higher dimensional spacetimes to allow
a study of the effect of number of dimensions on the possible final outcome of
the collapse in terms of either a black hole or naked singularity. No
restriction is adopted on the number of dimensions, and other limiting
assumptions such as self-similarity of spacetime are avoided, in order to keep
the treatment general. Our methodology allows to consider to an extent the
genericity and stability aspects related to the occurrence of naked
singularities in gravitational collapse.Comment: Revtex4, The replaced version matches the published on
An Implicit Lagrangean Code for Spherically Symmetric General Relativistic Hydrodynamics with an Approximate Riemann Solver
An implicit Lagrangian hydrodynamics code for general relativistic spherical
collapse is presented. This scheme is based on an approximate linearized
Riemann solver (Roe type scheme). This code is aimed especially at the
calculation of the late phase of collapse-driven supernovae and the nascent
neutron star, where there is a remarkable contrast between the dynamical time
scale of the proto-neutron star and the diffusion time scale of neutrinos,
without such severe limitation of the Courant condition at the center of the
neutron star. Several standard test calculations have been done. Two other
adiabatic simulations have also been done in order to test the performance of
the code in the context of the collapse-driven supernovae. It is found that the
time step can be extended far beyond the Courant limitation at the center of
the neutron star. The details of the scheme and the results of these test
calculations are discussed.Comment: AASTeX v4.0, 24 pages, 13 figures on request from
[email protected], submitted to Ap
Intense Electromagnetic Outbursts from Collapsing Hypermassive Neutron Stars
We study the gravitational collapse of a magnetized neutron star using a
novel numerical approach able to capture both the dynamics of the star and the
behavior of the surrounding plasma. In this approach, a fully general
relativistic magnetohydrodynamics implementation models the collapse of the
star and provides appropriate boundary conditions to a force-free model which
describes the stellar exterior. We validate this strategy by comparing with
known results for the rotating monopole and aligned rotator solutions and then
apply it to study both rotating and non-rotating stellar collapse scenarios,
and contrast the behavior with what is obtained when employing the
electrovacuum approximation outside the star. The non-rotating electrovacuum
collapse is shown to agree qualitatively with a Newtonian model of the
electromagnetic field outside a collapsing star. We illustrate and discuss a
fundamental difference between the force-free and electrovacuum solutions,
involving the appearance of large zones of electric-dominated field in the
vacuum case. This provides a clear demonstration of how dissipative
singularities appear generically in the non-linear time-evolution of force-free
fluids. In both the rotating and non-rotating cases, our simulations indicate
that the collapse induces a strong electromagnetic transient. In the case of
sub-millisecond rotation, the magnetic field experiences strong winding and the
transient carries much more energy. This result has important implications for
models of gamma-ray bursts.Comment: 28 pages, 20 figures (quality lowered to reduce sizes). Improved
initial data and matching condition results in a lower, but still important,
energy emission. Added appendix with a discussion on effects of transition
laye
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