14,404 research outputs found

    Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

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    The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid Ansatz. This is a straight non-oscillating string, radially disposed, which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass2^2) (Regge) relation for the planetoids, which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the author

    Strings in Cosmological and Black Hole Backgrounds: Ring Solutions

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    The string equations of motion and constraints are solved for a ring shaped Ansatz in cosmological and black hole spacetimes. In FRW universes with arbitrary power behavior [R(X^0) = a\;|X^0|^{\a}\, ], the asymptotic form of the solution is found for both X00X^0 \to 0 and X0X^0 \to \infty and we plot the numerical solution for all times. Right after the big bang (X0=0X^0 = 0), the string energy decreasess as R(X0)1 R(X^0)^{-1} and the string size grows as R(X0) R(X^0) for 01 0 1 . Very soon [ X01 X^0 \sim 1 ] , the ring reaches its oscillatory regime with frequency equal to the winding and constant size and energy. This picture holds for all values of \a including string vacua (for which, asymptotically, \a = 1). In addition, an exact non-oscillatory ring solution is found. For black hole spacetimes (Schwarzschild, Reissner-Nordstr\oo m and stringy), we solve for ring strings moving towards the center. Depending on their initial conditions (essentially the oscillation phase), they are are absorbed or not by Schwarzschild black holes. The phenomenon of particle transmutation is explicitly observed (for rings not swallowed by the hole). An effective horizon is noticed for the rings. Exact and explicit ring solutions inside the horizon(s) are found. They may be interpreted as strings propagating between the different universes described by the full black hole manifold.Comment: Paris preprint PAR-LPTHE-93/43. Uses phyzzx. Includes figures. Text and figures compressed using uufile

    Multi-String Solutions by Soliton Methods in De Sitter Spacetime

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    {\bf Exact} solutions of the string equations of motion and constraints are {\bf systematically} constructed in de Sitter spacetime using the dressing method of soliton theory. The string dynamics in de Sitter spacetime is integrable due to the associated linear system. We start from an exact string solution q(0)q_{(0)} and the associated solution of the linear system Ψ(0)(λ)\Psi^{(0)} (\lambda), and we construct a new solution Ψ(λ)\Psi(\lambda) differing from Ψ(0)(λ)\Psi^{(0)}(\lambda) by a rational matrix in λ\lambda with at least four poles λ0,1/λ0,λ0,1/λ0\lambda_{0},1/\lambda_{0},\lambda_{0}^*,1/\lambda_{0}^*. The periodi- city condition for closed strings restrict λ0\lambda _{0} to discrete values expressed in terms of Pythagorean numbers. Here we explicitly construct solu- tions depending on (2+1)(2+1)-spacetime coordinates, two arbitrary complex numbers (the 'polarization vector') and two integers (n,m)(n,m) which determine the string windings in the space. The solutions are depicted in the hyperboloid coor- dinates qq and in comoving coordinates with the cosmic time TT. Despite of the fact that we have a single world sheet, our solutions describe {\bf multi- ple}(here five) different and independent strings; the world sheet time τ\tau turns to be a multivalued function of TT.(This has no analogue in flat space- time).One string is stable (its proper size tends to a constant for TT\to\infty , and its comoving size contracts); the other strings are unstable (their proper sizes blow up for TT\to\infty, while their comoving sizes tend to cons- tants). These solutions (even the stable strings) do not oscillate in time. The interpretation of these solutions and their dynamics in terms of the sinh- Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under reques

    String dynamics in cosmological and black hole backgrounds: The null string expansion

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    We study the classical dynamics of a bosonic string in the DD--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet τ\tau--coordinate is given by X0(σ,τ)=q(σ)τ11+2β+c2B0(σ,τ)+X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots, B0(σ,τ)=kbk(σ)τkB^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k where bk(σ)b_k(\sigma) are given by Eqs.\ (3.15), and β\beta is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. RηβR\sim\eta^\beta. The string proper size, at first order in the fluctuations, grows like the conformal factor R(η)R(\eta) and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime DD generic. In the null string expansion, the radial, azimuthal, and time coordinates (r,ϕ,t)(r,\phi,t) are r=nAn1(σ)(τ)2n/(D+1) ,r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~, ϕ=nAn3(σ)(τ)(D5+2n)/(D+1) ,\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~, and t=nAn0(σ)(τ)1+2n(D3)/(D+1) .t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~. The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at r=0r=0. First and higher order string perturbations contribute with higher powers of τ\tau. The integrated string energy-momentum tensor corresponds to that of a null fluid in D1D-1 dimensions. As the string approaches the r=0r=0 singularity its proper size grows indefinitely like (τ)(D3)/(D+1)\sim(-\tau)^{-(D-3)/(D+1)}. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure

    Strings Propagating in the 2+1 Dimensional Black Hole Anti de Sitter Spacetime

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    We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at r=0.r=0. We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at r=0.r=0. We find the exact general solution for the circular string motion in all these backgrounds, it is given closely and completely in terms of elliptic functions. For the non-rotating black hole backgrounds the circular strings have a maximal bounded size rm,r_m, they contract and collapse into r=0.r=0. No indefinitely growing strings, neither multi-string solutions are present in these backgrounds. In rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the presence of angular momentum prevents the string from collapsing into r=0.r=0. The circular string motion is also completely solved in the black hole de Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS spacetime), in which expanding unbounded strings and multi-string solutions appear.Comment: Latex, 54 pages + 2 tables and 4 figures (not included). PARIS-DEMIRM 94/01

    Effects of regulation on a self-organized market

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    Adapting a simple biological model, we study the effects of control on the market. Companies are depicted as sites on a lattice and labelled by a fitness parameter (some `company-size' indicator). The chance of survival of a company on the market at any given time is related to its fitness, its position on the lattice and on some particular external influence, which may be considered to represent regulation from governments or central banks. The latter is rendered as a penalty for companies which show a very fast betterment in fitness space. As a result, we find that the introduction of regulation on the market contributes to lower the average fitness of companies.Comment: 7 pages, 2 figure