14,404 research outputs found

### Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

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/(mass$^2$) (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

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 $X^0 \to 0$ and $X^0 \to \infty$ and we plot the
numerical solution for all times. Right after the big bang ($X^0 = 0$), the
string energy decreasess as $R(X^0)^{-1}$ and the string size grows as $R(X^0)$ for $0 1$. Very
soon [ $X^0 \sim 1$] , 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

{\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 $q_{(0)}$ and the associated solution of the linear system $\Psi^{(0)}
(\lambda)$, and we construct a new solution $\Psi(\lambda)$ differing from
$\Psi^{(0)}(\lambda)$ by a rational matrix in $\lambda$ with at least four
poles $\lambda_{0},1/\lambda_{0},\lambda_{0}^*,1/\lambda_{0}^*$. The periodi-
city condition for closed strings restrict $\lambda _{0}$ to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on $(2+1)$-spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers $(n,m)$ which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates $q$ and in comoving coordinates with the cosmic time $T$. 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 $\tau$
turns to be a multivalued function of $T$.(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for $T\to\infty$, and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for $T\to\infty$, 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

We study the classical dynamics of a bosonic string in the $D$--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 $\tau$--coordinate
is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma,
\tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$
are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string
proper size, at first order in the fluctuations, grows like the conformal
factor $R(\eta)$ 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 $D$ generic. In the null
string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are
$r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n
A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n}
(\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at $r=0$. First and
higher order string perturbations contribute with higher powers of $\tau$. The
integrated string energy-momentum tensor corresponds to that of a null fluid in
$D-1$ dimensions. As the string approaches the $r=0$ singularity its proper
size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. 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

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 $r=0.$ 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 $r=0.$ 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 $r_m,$ they contract and collapse into $r=0.$ 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 $r=0.$
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

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

- …