42 research outputs found

### Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked
singularity formation from an initial density profile which is physically
reasonable. In this paper, we show that explosive radiation is emitted during
the formation process of the naked singularity.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a
Rapid Communicatio

### Semiclassical Instability of the Cauchy Horizon in Self-Similar Collapse

Generic spherically symmetric self-similar collapse results in strong
naked-singularity formation. In this paper we are concerned with particle
creation during a naked-singularity formation in spherically symmetric
self-similar collapse without specifying the collapsing matter. In the generic
case, the power of particle emission is found to be proportional to the inverse
square of the remaining time to the Cauchy horizon (CH). The constant of
proportion can be arbitrarily large in the limit to marginally naked
singularity. Therefore, the unbounded power is especially striking in the case
that an event horizon is very close to the CH because the emitted energy can be
arbitrarily large in spite of a cutoff expected from quantum gravity. Above
results suggest the instability of the CH in spherically symmetric self-similar
spacetime from quantum field theory and seem to support the existence of a
semiclassical cosmic censor. The divergence of redshifts and blueshifts of
emitted particles is found to cause the divergence of power to positive or
negative infinity, depending on the coupling manner of scalar fields to
gravity. On the other hand, it is found that there is a special class of
self-similar spacetimes in which the semiclassical instability of the CH is not
efficient. The analyses in this paper are based on the geometric optics
approximation, which is justified in two dimensions but needs justification in
four dimensions.Comment: 14 pages, 4 figures, minor errors corrected and some sentences added
in the introduction, accepted for publication in Physical Review

### No Go Theorem for Kinematic Self-Similarity with A Polytropic Equation of State

We have investigated spherically symmetric spacetimes which contain a perfect
fluid obeying the polytropic equation of state and admit a kinematic
self-similar vector of the second kind which is neither parallel nor orthogonal
to the fluid flow. We have assumed two kinds of polytropic equations of state
and shown in general relativity that such spacetimes must be vacuum.Comment: 5 pages, no figures. Revtex. One word added to the title. Final
version to appear in Physical Review D as a Brief Repor

### Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when
arbitrarily small perfect fluid pressures are introduced in the classic black
hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) [1].
This extends a previous result on tangential pressures [2] to the more
physically realistic scenario of perfect fluid collapse. The existence of
classes of pressure perturbations is shown explicitly, which has the property
that injecting any smallest pressure changes the final fate of the dynamical
collapse from a black hole to a naked singularity. It is therefore seen that
any smallest neighborhood of the OSD model, in the space of initial data,
contains collapse evolutions that go to a naked singularity outcome. This gives
an intriguing insight on the nature of naked singularity formation in
gravitational collapse.Comment: 7 pages, 1 figure, several modifications to match published version
on GR

### Power, energy, and spectrum of a naked singularity explosion

Naked singularity occurs in the gravitational collapse of an inhomogeneous
dust ball from an initial density profile which is physically reasonable. We
show that explosive radiation is emitted during the formation process of the
naked singularity. The energy flux is proportional to $(t_{\rm CH}-t)^{-3/2}$
for a minimally coupled massless scalar field, while is proportional to
$(t_{\rm CH}-t)^{-1}$ for a conformally coupled massless scalar field, where
$t_{\rm CH}-t$ is the `remained time' until the distant observer could observe
the singularity if the naked singularity was formed. As a consequence, the
radiated energy grows unboundedly for both scalar fields. The amount of the
power and the energy depends on parameters which characterize the initial
density profile but do not depend on the gravitational mass of the cloud. In
particular, there is characteristic frequency $\nu_{s}$ of singularity above
which the divergent energy is radiated. The energy flux is dominated by
particles of which the wave length is about $t_{\rm CH}-t$ at each moment. The
observed total spectrum is nonthermal, i.e., $\nu dN/d\nu \sim
(\nu/\nu_{s})^{-1}$ for $\nu>\nu_{s}$. If the naked singularity formation could
continue until a considerable fraction of the total energy of the dust cloud is
radiated, the radiated energy would reach about $10^{54}(M/M_{\odot})$ erg. The
calculations are based on the geometrical optics approximation which turns out
to be consistent as a rough order estimate. The analysis does not depend on
whether or not the naked singularity occurs in its exact meaning. This
phenomenon may provide a new candidate for a source of ultra high energy cosmic
rays or a central engine of gamma ray bursts.Comment: 34 pages, 13 postscript figures included, to appear in Phys. Rev. D,
grammatical errors correcte

### Black holes vs. naked singularities formation in collapsing Einstein's clusters

Non-static, spherically symmetric clusters of counter-rotating particles, of
the type first introduced by Einstein, are analysed here. The initial data
space can be parameterized in terms of three arbitrary functions, namely;
initial density, velocity and angular momentum profiles. The final state of
collapse, black hole or naked singularity, turns out to depend on the order of
the first non-vanishing derivatives of such functions at the centre. The work
extends recent results by Harada, Iguchi and Nakao.Comment: 13 pages, LaTeX format. To appear in Physical Review

### Spherical Universes with Anisotropic Pressure

Einstein's equations are solved for spherically symmetric universes composed
of dust with tangential pressure provided by angular momentum, L(R), which
differs from shell to shell. The metric is given in terms of the shell label,
R, and the proper time, tau, experienced by the dust particles. The general
solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R).
The solution is described by quadratures, which are in general elliptic
integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution.
We present a discussion of the types of solution, and some examples. The
relationship to Einstein clusters and the significance for gravitational
collapse is also discussed.Comment: 24 pages, 11 figures, accepted for publication in Classical and
Quantum Gravit

### Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

It was recently shown that the metric functions which describe a spherically
symmetric space-time with vanishing radial pressure can be explicitly
integrated. We investigate the nakedness and curvature strength of the
shell-focusing singularity in that space-time. If the singularity is naked, the
relation between the circumferential radius and the Misner-Sharp mass is given
by $R\approx 2y_{0} m^{\beta}$ with $1/3<\beta\le 1$ along the first radial
null geodesic from the singularity. The $\beta$ is closely related to the
curvature strength of the naked singularity. For example, for the outgoing or
ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds,
then $\beta$ must be equal to 1. We define the ``gravity dominance condition''
(GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and
the limiting focusing condition (LFC) by Kr\'olak hold for $\beta=1$ and
$y_{0}\ne 1$, not SCC but only LFC holds for $1/2\le \beta <1$, and neither
holds for $1/3<\beta <1/2$, for the null geodesic. On the other hand, if GDC is
satisfied for the timelike geodesic $r=0$, both SCC and LFC are satisfied for
the timelike geodesic, irrespective of the value of $\beta$. Several examples
are also discussed.Comment: 11 pages, Accepted for Publication in Classical and Quantum Gravity,
References Updated, Grammatical Errors Correcte

### Self-similar and charged spheres in the diffusion approximation

We study spherical, charged and self--similar distributions of matter in the
diffusion approximation. We propose a simple, dynamic but physically meaningful
solution. For such a solution we obtain a model in which the distribution
becomes static and changes to dust. The collapse is halted with damped mass
oscillations about the absolute value of the total charge.Comment: 15 pages, 7 figure

### Relativistic shells: Dynamics, horizons, and shell crossing

We consider the dynamics of timelike spherical thin matter shells in vacuum.
A general formalism for thin shells matching two arbitrary spherical spacetimes
is derived, and subsequently specialized to the vacuum case. We first examine
the relative motion of two dust shells by focusing on the dynamics of the
exterior shell, whereby the problem is reduced to that of a single shell with
different active Schwarzschild masses on each side. We then examine the
dynamics of shells with non-vanishing tangential pressure $p$, and show that
there are no stable--stationary, or otherwise--solutions for configurations
with a strictly linear barotropic equation of state, $p=\alpha\sigma$, where
$\sigma$ is the proper surface energy density and $\alpha\in(-1,1)$. For {\em
arbitrary} equations of state, we show that, provided the weak energy condition
holds, the strong energy condition is necessary and sufficient for stability.
We examine in detail the formation of trapped surfaces, and show explicitly
that a thin boundary layer causes the apparent horizon to evolve
discontinuously. Finally, we derive an analytical (necessary and sufficient)
condition for neighboring shells to cross, and compare the discrete shell model
with the well-known continuous Lema\^{\i}tre-Tolman-Bondi dust case.Comment: 25 pages, revtex4, 4 eps figs; published in Phys. Rev.