Collective Quantisation of a Gravitating Skyrmion

Collective quantisation of a B=1 gravitating skyrmion is described. The rotational and isorotational modes are quantised in the same manner as the skyrmion without gravity. It is shown in this paper how the static properties of nucleons such as masses, charge densities, magnetic moments are modified by the gravitational interaction.Comment: 10 pages, 9 figures, minor corrections, published versio

Skyrme Black Holes in the Isolated Horizons Formalism

We study static, spherically symmetric, Skyrme black holes in the context of the assumption that they can be viewed as bound states between ordinary bare black holes and solitons. This assumption and results stemming from the isolated horizons formalism lead to several conjectures about the static black hole solutions. These conjectures are tested against the Skyrme black hole solutions. It is shown that, while there is in general good agreement with the conjectures, a crucial aspect seems to violate one of the conjectures.Comment: Full journal version, 6 pages, 5 figure

The Cosmological Probability Density Function for Bianchi Class A Models in Quantum Supergravity

Nicolai's theorem suggests a simple stochastic interpetation for supersymmetric Euclidean quantum theories, without requiring any inner product to be defined on the space of states. In order to apply this idea to supergravity, we first reduce to a one-dimensional theory with local supersymmetry by the imposition of homogeneity conditions. We then make the supersymmetry rigid by imposing gauge conditions, and quantise to obtain the evolution equation for a time-dependent wave function. Owing to the inclusion of a certain boundary term in the classical action, and a careful treatment of the initial conditions, the evolution equation has the form of a Fokker-Planck equation. Of particular interest is the static solution, as this satisfies all the standard quantum constraints. This is naturally interpreted as a cosmological probability density function, and is found to coincide with the square of the magnitude of the conventional wave function for the wormhole state.Comment: 22 pages, Late

Energy Momentum Tensor in Conformal Field Theories Near a Boundary

The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary invariant. It is shown that the general solution may contain an arbitrary function of a single conformally invariant variable $v$, except in dimension 2. The functional dependence on $v$ is determined for free scalar and fermion fields in arbitrary dimension $d$ and also to leading order in the \vep expansion about $d=4$ for the non Gaussian fixed point in $\phi^4$ theory. The two point correlation function of the energy momentum tensor and a scalar field is also shown to have a unique expression in terms of $v$ and the overall coefficient is determined by the operator product expansion. The energy momentum tensor on a general curved manifold is further discussed by considering variations of the metric. In the presence of a boundary this procedure naturally defines extra boundary operators. By considering diffeomorphisms these are related to components of the energy momentum tensor on the boundary. The implications of Weyl invariance in this framework are also derived.Comment: 22 pages, TeX with epsf.tex, DAMTP/93-1. (original uuencoded file was corrupted enroute - resubmitted version has uuencoded figures pasted to the ended of the Plain TeX file

Internal structure of Skyrme black hole

We consider the internal structure of the Skyrme black hole under a static and spherically symmetric ansatz. $@u8(Be concentrate on solutions with the node number one and with the "winding" number zero, where there exist two solutions for each horizon radius; one solution is stable and the other is unstable against linear perturbation. We find that a generic solution exhibits an oscillating behavior near the sigularity, as similar to a solution in the Einstein-Yang-Mills (EYM) system, independently to stability of the solution. Comparing it with that in the EYM system, this oscillation becomes mild because of the mass term of the Skyrme field. We also find Schwarzschild-like exceptional solutions where no oscillating behavior is seen. Contrary to the EYM system where there is one such solution branch if the node number is fixed, there are two branches corresponding to the stable and the unstable ones.Comment: 5 pages, 4 figures, some contents adde

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

Regular and Black Hole Solutions in the Einstein-Skyrme Theory with Negative Cosmological Constant

We study spherically symmetric regular and black hole solutions in the Einstein-Skyrme theory with a negative cosmological constant. The Skyrme field configuration depends on the value of the cosmological constant in a similar manner to effectively varying the gravitational constant. We find the maximum value of the cosmological constant above which there exists no solution. The properties of the solutions are discussed in comparison with the asymptotically flat solutions. The stability is investigated in detail by solving the linearly perturbed equation numerically. We show that there exists a critical value of the cosmological constant above which the solution in the branch representing unstable configuration in the asymptotically flat spacetime turns to be linearly stable.Comment: 10 pages, 9 figures, comments and one reference added, to appear in Class.Quant.Gra

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)$\times$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 ($M_{g}$-$r_{h}$) 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