10,992 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) (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 Next To and Inside Black Holes
The string equations of motion and constraints are solved near the horizon
and near the singularity of a Schwarzschild black hole. In a conformal gauge
such that ( = worldsheet time coordinate) corresponds to the
horizon () or to the black hole singularity (), the string
coordinates express in power series in near the horizon and in power
series in around . We compute the string invariant size and
the string energy-momentum tensor. Near the horizon both are finite and
analytic. Near the black hole singularity, the string size, the string energy
and the transverse pressures (in the angular directions) tend to infinity as
. To leading order near , the string behaves as two dimensional
radiation. This two spatial dimensions are describing the sphere in the
Schwarzschild manifold.Comment: RevTex, 19 pages without figure
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --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 --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor 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 generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
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
An analytical proof of Hardy-like inequalities related to the Dirac operator
We prove some sharp Hardy type inequalities related to the Dirac operator by
elementary, direct methods. Some of these inequalities have been obtained
previously using spectral information about the Dirac-Coulomb operator. Our
results are stated under optimal conditions on the asymptotics of the
potentials near zero and near infinity.Comment: LaTex, 22 page
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 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 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 they contract and collapse into 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
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
Circular String-Instabilities in Curved Spacetime
We investigate the connection between curved spacetime and the emergence of
string-instabilities, following the approach developed by Loust\'{o} and
S\'{a}nchez for de Sitter and black hole spacetimes. We analyse the linearised
equations determining the comoving physical (transverse) perturbations on
circular strings embedded in Schwarzschild, Reissner-Nordstr\"{o}m and de
Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow
infinitely for (ring-collapse), while the "angular"
perturbations are bounded in this limit. For we find that
the perturbations in both physical directions (perpendicular to the string
world-sheet in 4 dimensions) blow up in the case of de Sitter space. This
confirms results recently obtained by Loust\'{o} and S\'{a}nchez who considered
perturbations around the string center of mass.Comment: 24 pages Latex + 2 figures (not included). Observatoire de Paris,
Meudon No. 9305
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 and and we plot the
numerical solution for all times. Right after the big bang (), the
string energy decreasess as and the string size grows as for . Very
soon [ ] , 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
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