41 research outputs found
Statistical properties of stock order books: empirical results and models
We investigate several statistical properties of the order book of three
liquid stocks of the Paris Bourse. The results are to a large degree
independent of the stock studied. The most interesting features concern (i) the
statistics of incoming limit order prices, which follows a power-law around the
current price with a diverging mean; and (ii) the humped shape of the average
order book, which can be quantitatively reproduced using a `zero intelligence'
numerical model, and qualitatively predicted using a simple approximation.Comment: Revised version, 10 pages, 4 .eps figures. to appear in Quantitative
Financ
Non-Abelian Black Holes in Brans-Dicke Theory
We find a black hole solution with non-Abelian field in Brans-Dicke theory.
It is an extension of non-Abelian black hole in general relativity. We discuss
two non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and
the SU(2)SU(2) Skyrme field. In both cases, as in general relativity,
there are two branches of solutions, i.e., two black hole solutions with the
same horizon radius. Masses of both black holes are always smaller than those
in general relativity. A cusp structure in the mass-horizon radius
(-) diagram, which is a typical symptom of stability change in
catastrophe theory, does not appear in the Brans-Dicke frame but is found in
the Einstein conformal frame. This suggests that catastrophe theory may be
simply applied for a stability analysis as it is if we use the variables in the
Einstein frame. We also discuss the effects of the Brans-Dicke scalar field on
black hole structure.Comment: 31 pages, revtex, 21 figure
Non-Abelian Black Holes and Catastrophe Theory I : Neutral Type
We re-analyze the globally neutral non-Abelian black holes and present a
unified picture, classifying them into two types; Type I (black holes with
massless non-Abelian field) and Type II (black holes with ``massive"
non-Abelian field). For the Type II, there are two branches: The black hole in
the high-entropy branch is ``stable" and almost neutral, while that in the low
entropy branch, which is similar to the Type I, is unstable and locally
charged. To analyze their stabilities, we adopt the catastrophe theoretic
method, which reveals us a universal picture of stability of the black holes.
It is shown that the isolated Type II black hole has a fold catastrophe
structure.
In a heat bath system, the Type I black hole shows a cusp catastrophe, while
the Type II has both fold and cusp catastrophe.Comment: 27pages, LaTex style, WU-AP/39/94. Figures are available (hard
copies) upon requests [[email protected] (T.Torii)
Dilatonic Black Holes with Gauss-Bonnet Term
We discuss black holes in an effective theory derived from a superstring
model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term.
Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of
spherically symmetric solutions, i.e., a neutral, an electrically charged, a
magnetically charged and a ``colored'' black hole, and discuss their
thermodynamical properties and fate via the Hawking evaporation process. For
neutral and electrically charged black holes, we find critical point and a
singular end point. Below the mass corresponding to the critical point,
nosolution exists, while the curvature on the horizon diverges and anaked
singularity appears at the singular point. A cusp structure in the mass-entropy
diagram is found at the critical point and black holes on the branch between
the critical and singular points become unstable. For magnetically charged and
``colored" black holes, the solution becomes singular just at the end point
with a finite mass. Because the black hole temperature is always finite even at
the critical point or the singular point, we may conclude that the evaporation
process will not be stopped even at the critical point or the singular point,
and the black hole will move to a dynamical evaporation phase or a naked
singularity will appear.Comment: 31pages, 11figures, LaTex styl
Heat kernel coefficients for chiral bag boundary conditions
We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2)
where P is an operator of Dirac type, f is an auxiliary smooth smearing
function which is used to localize the problem, and chiral bag boundary
conditions are imposed. Special case calculations, functorial methods and the
theory of zeta and eta invariants are used to obtain the boundary part of the
heat-kernel coefficients a1 and a2.Comment: Published in J. Phys. A38, 2259-2276 (2005). Record without file
already exists on the SLAC recor
Perturbations of global monopoles as a black hole's hair
We study the stability of a spherically symmetric black hole with a global
monopole hair. Asymptotically the spacetime is flat but has a deficit solid
angle which depends on the vacuum expectation value of the scalar field. When
the vacuum expectation value is larger than a certain critical value, this
spacetime has a cosmological event horizon. We investigate the stability of
these solutions against the spherical and polar perturbations and confirm that
the global monopole hair is stable in both cases. Although we consider some
particular modes in the polar case, our analysis suggests the conservation of
the "topological charge" in the presence of the event horizons and violation of
black hole no-hair conjecture in asymptotically non-flat spacetime.Comment: 11 pages, 2 figures, some descriptions were improve
Euclidean Black Hole Vortices
We argue the existence of solutions of the Euclidean Einstein equations that
correspond to a vortex sitting at the horizon of a black hole. We find the
asymptotic behaviours, at the horizon and at infinity, of vortex solutions for
the gauge and scalar fields in an abelian Higgs model on a Euclidean
Schwarzschild background and interpolate between them by integrating the
equations numerically. Calculating the backreaction shows that the effect of
the vortex is to cut a slice out of the Euclidean Schwarzschild geometry.
Consequences of these solutions for black hole thermodynamics are discussed.Comment: 24 page
On the absence of scalar hair for charged rotating blackholes in non minimally coupled theories
In this work we check the validity of the no scalar hair theorem in charged
axisymmetric stationary black holes for a wide class of scalar tensor theories.Comment: Revtex style, 11 pages, major rivisions done, appendix added, title
change
Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries
This paper studies the one-loop expansion of the amplitudes of
electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere,
recently considered in perturbative quantum cosmology, by using zeta-function
regularization. For a specific choice of gauge-averaging functional, the
contributions to the full zeta value owed to physical degrees of freedom,
decoupled gauge mode, coupled gauge modes and Faddeev-Popov ghost field are
derived in detail, and alternative choices for such a functional are also
studied. This analysis enables one to get a better understanding of different
quantization techniques for gauge fields and gravitation in the presence of
boundaries.Comment: 41 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, pages 905-926, April 1994. The author wants to apologize
for the delay in circulating the file, due to technical problems now fixe