4,497 research outputs found
Theory of Phase Transition in the Evolutionary Minority Game
We discover the mechanism for the transition from self-segregation (into
opposing groups) to clustering (towards cautious behaviors) in the evolutionary
minority game (EMG). The mechanism is illustrated with a statistical mechanics
analysis of a simplified EMG involving three groups of agents: two groups of
opposing agents and one group of cautious agents. Two key factors affect the
population distribution of the agents. One is the market impact (the
self-interaction), which has been identified previously. The other is the
market inefficiency due to the short-time imbalance in the number of agents
using opposite strategies. Large market impact favors "extreme" players who
choose fixed strategies, while large market inefficiency favors cautious
players. The phase transition depends on the number of agents (), the
reward-to-fine ratio (), as well as the wealth reduction threshold () for
switching strategy. When the rate for switching strategy is large, there is
strong clustering of cautious agents. On the other hand, when is small, the
market impact becomes large, and the extreme behavior is favored.Comment: 5 pages and 3 figure
Asymptotic tails of massive scalar fields in a stationary axisymmetric EMDA black hole geometry
The late-time tail behavior of massive scalar fields is studied analytically
in a stationary axisymmetric EMDA black hole geometry. It is shown that the
asymptotic behavior of massive perturbations is dominated by the oscillatory
inverse power-law decaying tail at the intermediate
late times, and by the asymptotic tail at asymptotically
late times. Our result seems to suggest that the intermediate tails and the asymptotically tails
may be quite general features for evolution of massive scalar fields in any
four dimensional asymptotically flat rotating black hole backgrounds.Comment: 6 page
Late-Time Evolution of Charged Gravitational Collapse and Decay of Charged Scalar Hair - II
We study analytically the initial value problem for a charged massless
scalar-field on a Reissner-Nordstr\"om spacetime. Using the technique of
spectral decomposition we extend recent results on this problem. Following the
no-hair theorem we reveal the dynamical physical mechanism by which the charged
hair is radiated away. We show that the charged perturbations decay according
to an inverse power-law behaviour at future timelike infinity and along future
null infinity. Along the future outer horizon we find an oscillatory inverse
power-law relaxation of the charged fields. We find that a charged black hole
becomes ``bald'' slower than a neutral one, due to the existence of charged
perturbations. Our results are also important to the study of mass-inflation
and the stability of Cauchy horizons during a dynamical gravitational collapse
of charged matter in which a charged black-hole is formed.Comment: Latex 15 pages, Revtex.st
Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations
We consider the late-time evolution of {\it gravitational} and
electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We
give a detailed analysis of the mode-coupling phenomena in rotating
gravitational collapse. A consequence of this phenomena is that the late-time
tail is dominated by modes which, in general, may have an angular distribution
different from the original one. In addition, we show that different types of
fields have {\it different} decaying rates. This result turns over the
traditional belief (which has been widely accepted during the last three
decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page
A note on the quantization of a multi-horizon black hole
We consider the quasinormal spectrum of a charged scalar field in the
(charged) Reissner-Nordstrom spacetime, which has two horizons. The spectrum is
characterized by two distinct families of asymptotic resonances. We suggest and
demonstrate the according to Bohr's correspondence principle and in agreement
with the Bekenstein-Mukhanov quantization scheme, one of these resonances
corresponds to a fundamental change of Delta A=4hbar ln2 in the surface area of
the black-hole outer horizon. The second asymptotic resonance is associated
with a fundamental change of Delta Atot=4hbar ln3 in the total area of the
black hole (in the sum of the surface areas of the inner and outer horizons),
in accordance with a suggestion of Makela and Repo.Comment: 6 page
Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole
We investigate the late-time tails of self-interacting (massive) scalar
fields in the spacetime of dilaton black hole. Following the no hair theorem we
examine the mechanism by which self-interacting scalar hair decay. We revealed
that the intermediate asymptotic behavior of the considered field perturbations
is dominated by an oscillatory inverse power-law decaying tail. The numerical
simulations showed that at the very late-time massive self-interacting scalar
hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.
Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
We consider a massless scalar field propagating in a weakly curved spacetime
whose metric is a solution to the linearized Einstein field equations. The
spacetime is assumed to be stationary and asymptotically flat, but no other
symmetries are imposed -- the spacetime can rotate and deviate strongly from
spherical symmetry. We prove that the late-time behavior of the scalar field is
identical to what it would be in a spherically-symmetric spacetime: it decays
in time according to an inverse power-law, with a power determined by the
angular profile of the initial wave packet (Price falloff theorem). The field's
late-time dynamics is insensitive to the nonspherical aspects of the metric,
and it is governed entirely by the spacetime's total gravitational mass; other
multipole moments, and in particular the spacetime's total angular momentum, do
not enter in the description of the field's late-time behavior. This extended
formulation of Price's falloff theorem appears to be at odds with previous
studies of radiative decay in the spacetime of a Kerr black hole. We show,
however, that the contradiction is only apparent, and that it is largely an
artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX
On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry
Loop quantum gravity can account for the Bekenstein-Hawking entropy of a
black hole provided a free parameter is chosen appropriately. Recently, it was
proposed that a new choice of the Immirzi parameter could predict both black
hole entropy and the frequencies of quasinormal modes in the large limit,
but at the price of changing the gauge group of the theory. In this note we use
a simple physical argument within loop quantum gravity to arrive at the same
value of the parameter. The argument uses strongly the necessity of having
fermions satisfying basic symmetry and conservation principles, and therefore
supports SU(2) as the relevant gauge group of the theory.Comment: 3 pages, revtex4, no figures, discussion expanded and references
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High-Order Contamination in the Tail of Gravitational Collapse
It is well known that the late-time behaviour of gravitational collapse is
{\it dominated} by an inverse power-law decaying tail. We calculate {\it
higher-order corrections} to this power-law behaviour in a spherically
symmetric gravitational collapse. The dominant ``contamination'' is shown to
die off at late times as . This decay rate is much {\it
slower} than has been considered so far. It implies, for instance, that an
`exact' (numerical) determination of the power index to within
requires extremely long integration times of order . We show that the
leading order fingerprint of the black-hole electric {\it charge} is of order
.Comment: 12 pages, 2 figure
Dyonic Kerr-Newman black holes, complex scalar field and Cosmic Censorship
We construct a gedanken experiment, in which a weak wave packet of the
complex massive scalar field interacts with a four-parameter (mass, angular
momentum, electric and magnetic charges) Kerr-Newman black hole. We show that
this interaction cannot convert an extreme the black hole into a naked
sigularity for any black hole parameters and any generic wave packet
configuration. The analysis therefore provides support for the weak cosmic
censorship conjecture.Comment: Refined emphasis on the weak cosmic censorship conjecture,
conclusions otherwise unchanged. Also, two sections merged, literature review
updated, references added, a few typos correcte
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