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 ($N$), the reward-to-fine ratio ($R$), as well as the wealth reduction threshold ($d$) for switching strategy. When the rate for switching strategy is large, there is strong clustering of cautious agents. On the other hand, when $N$ 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 $t^{-(l+3/2)}\sin(\mu t)$ at the intermediate late times, and by the asymptotic tail $t^{-5/6}\sin(\mu t)$ at asymptotically late times. Our result seems to suggest that the intermediate tails $t^{-(l+3/2)}\sin(\mu t)$ and the asymptotically tails $t^{-5/6} \sin(\mu t)$ 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 $n$ 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 adde

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 $M^2t^{-4}\ln(t/M)$. 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 $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.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