1,546 research outputs found
An Analytic Model with Critical Behavior in Black Hole Formation
A simple analytic model is presented which exhibits a critical behavior in
black hole formation, namely, collapse of a thin shell coupled with outgoing
null fluid. It is seen that the critical behavior is caused by the
gravitational nonlinearity near the event horizon. We calculate the value of
the critical exponent analytically and find that it is very dependent on the
coupling constants of the system.Comment: 21pp., ReVTeX, 7 figures (postscript, compressed and uuencoded),
TIT/HEP-266/COSMO-4
Self-Similar Collapse of Scalar Field in Higher Dimensions
This paper constructs continuously self-similar solution of a spherically
symmetric gravitational collapse of a scalar field in n dimensions. The
qualitative behavior of these solutions is explained, and closed-form answers
are provided where possible. Equivalence of scalar field couplings is used to
show a way to generalize minimally coupled scalar field solutions to the model
with general coupling.Comment: RevTex 3.1, 15 pages, 3 figures; references adde
Surface gravity in dynamical spherically symmetric spacetimes
A definition of surface gravity at the apparent horizon of dynamical
spherically symmetric spacetimes is proposed. It is based on a unique foliation
by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can
be interpreted as the phase of a light wave uniformly emitted by some far-away
static observer. The definition gives back the accepted value of surface
gravity in the static case by virtue of its nonlocal character. Although the
definition is motivated by the behavior of outgoing null rays, it turns out
that there is a simple connection between the generalized surface gravity, the
acceleration of any radially moving observer, and the observed frequency change
of the infalling light signal. In particular, this gives a practical and simple
method of how any geodesic observer can determine surface gravity by measuring
only the redshift of the infalling light wave. The surface gravity can be
expressed as an integral of matter field quantities along an ingoing null line,
which shows that it is a continuous function along the apparent horizon. A
formula for the area change of the apparent horizon is presented, and the
possibility of thermodynamical interpretation is discussed. Finally, concrete
expressions of surface gravity are given for a number of four-dimensional and
two-dimensional dynamical black hole solutions.Comment: 35 pages, revtex, 3 figures included using eps
Self-Similar Collapse of Conformally Coupled Scalar Fields
A massless scalar field minimally coupled to the gravitational field in a
simplified spherical symmetry is discussed. It is shown that, in this case, the
solution found by Roberts, describing a scalar field collapse, is in fact the
most general one. Taking that solution as departure point, a study of the
gravitational collapse for the self-similar conformal case is presented.Comment: 9 pages, accepted for publication, Classical and Quantum Gravity.
Available at http://dft.if.uerj.br/preprint/e-17.tex or at
ftp://dft.if.uerj.br/preprint/e-17.tex . Figures can be obtained on request
at [email protected]
An extreme critical space-time: echoing and black-hole perturbations
A homothetic, static, spherically symmetric solution to the massless
Einstein- Klein-Gordon equations is described. There is a curvature singularity
which is central, null, bifurcate and marginally trapped. The space-time is
therefore extreme in the sense of lying at the threshold between black holes
and naked singularities, just avoiding both. A linear perturbation analysis
reveals two types of dominant mode. One breaks the continuous self-similarity
by periodic terms reminiscent of discrete self-similarity, with echoing period
within a few percent of the value observed numerically in near-critical
gravitational collapse. The other dominant mode explicitly produces a black
hole, white hole, eternally naked singularity or regular dispersal, the latter
indicating that the background is critical. The black hole is not static but
has constant area, the corresponding mass being linear in the perturbation
amplitudes, explicitly determining a unit critical exponent. It is argued that
a central null singularity may be a feature of critical gravitational collapse.Comment: 6 revtex pages, 6 eps figure
On critical behaviour in gravitational collapse
We give an approach to studying the critical behaviour that has been observed
in numerical studies of gravitational collapse. These studies suggest, among
other things, that black holes initially form with infinitesimal mass. We show
generally how a black hole mass formula can be extracted from a transcendental
equation.
Using our approach, we give an explicit one parameter set of metrics that are
asymptotically flat and describe the collapse of apriori unspecified but
physical matter fields. The black hole mass formula obtained from this metric
exhibits a mass gap - that is, at the onset of black hole formation, the mass
is finite and non-zero.Comment: 11 pages, RevTex, 2 figures (available from VH
Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field
This paper studies the perturbations of the continuously self-similar
critical solution of the gravitational collapse of a massless scalar field
(Roberts solution). The perturbation equations are derived and solved exactly.
The perturbation spectrum is found to be not discrete, but occupying continuous
region of the complex plane. The renormalization group calculation gives the
value of the mass-scaling exponent equal to 1.Comment: 12 pages, RevTeX 3.1, 1 figur
Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model
We present an exact collapsing solution to 2+1 gravity with a negative
cosmological constant minimally coupled to a massless scalar field, which
exhibits physical properties making it a candidate critical solution. We
discuss its global causal structure and its symmetries in relation with those
of the corresponding continously self-similar solution derived in the
case. Linear perturbations on this background lead to approximate
black hole solutions. The critical exponent is found to be .Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and
5. The value of the critical exponent has been revised to \gamma = 2/
Espacialização da pecuária de corte sul-mato-grossense.
A economia do Estado de Mato Grosso do Sul baseia-se principalmente na agricultura e pecuária, e o estado é subdivido em quatro mesorregiões: Centro-Norte, Pantanal, Sudoeste e Leste. Para espacializar a produção da pecuária bovina sul-mato-grossense, foram usados dados censitários e geocódigos municipais do IBGE e procedimentos do sistema de informação geográfica (SIG). As mesorregiões Leste e Sudoeste comportam o maior número de cabeças, da ordem de seis milhões. A mesorregião do Pantanal possui imensas áreas alagadas e favorece a exploração extensiva, e a mesorregião Centro-Norte, localizada mais próxima aos grandes mercados consumidores, têm cerca de quatro milhões de cabeças. A taxa geométrica de crescimento (TGC) do rebanho bovino de 2006 a 2011 apresenta padrão irregular, com variação de -6,86 a +7,31, -5,60 a +13,33, -2,65 a +6,65 e -5,15 a +2,45 para as regiões Pantanal, Centro-Norte, Sudoeste e Leste, respectivamente. Em termos nacionais, as projeções da TGC (2007 a 2023) para consumo e exportação são da ordem de 30% e 22,4%, respectivamente, enquanto a TGC para produção nesse mesmo período é da ordem de 18,4%. Esses números representam menos oferta interna e potencial aquecimento dos preços domésticos, contribuindo, assim, para um possível aumento da taxa de inflação no período analisado
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