8,900 research outputs found
Planetoid strings : solutions and perturbations
A novel ansatz for solving the string equations of motion and constraints in
generic curved backgrounds, namely the planetoid ansatz, was proposed recently
by some authors. We construct several specific examples of planetoid strings in
curved backgrounds which include Lorentzian wormholes, spherical Rindler
spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is
performed and the Regge relations for the planetoids are obtained. The general
equations for the study of small perturbations about these solutions are
written down using the standard, manifestly covariant formalism. Applications
to special cases such as those of planetoid strings in Minkowski and spherical
Rindler spacetimes are also presented.Comment: 24 pages (including two figures), RevTex, expanded and figures adde
A method for solve integrable spin chains combining different representations
A non homogeneous spin chain in the representations and
of is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
PACS: 75.10.Jm, 05.50+q 02.20 SvComment: PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev.
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
Exact String Solutions in Nontrivial Backgrounds
We show how the classical string dynamics in -dimensional gravity
background can be reduced to the dynamics of a massless particle constrained on
a certain surface whenever there exists at least one Killing vector for the
background metric. We obtain a number of sufficient conditions, which ensure
the existence of exact solutions to the equations of motion and constraints.
These results are extended to include the Kalb-Ramond background. The
-brane dynamics is also analyzed and exact solutions are found. Finally, we
illustrate our considerations with several examples in different dimensions.
All this also applies to the tensionless strings.Comment: 22 pages, LaTeX, no figures; V2:Comments and references added;
V3:Discussion on the properties of the obtained solutions extended, a
reference and acknowledgment added; V4:The references renumbered, to appear
in Phys Rev.
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
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 and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . 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
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , 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 Instabilities in Black Hole Spacetimes
We study the emergence of string instabilities in - dimensional black
hole spacetimes (Schwarzschild and Reissner - Nordstr\o m), and De Sitter space
(in static coordinates to allow a better comparison with the black hole case).
We solve the first order string fluctuations around the center of mass motion
at spatial infinity, near the horizon and at the spacetime singularity. We find
that the time components are always well behaved in the three regions and in
the three backgrounds. The radial components are {\it unstable}: imaginary
frequencies develop in the oscillatory modes near the horizon, and the
evolution is like , , near the spacetime
singularity, , where the world - sheet time , and the
proper string length grows infinitely. In the Schwarzschild black hole, the
angular components are always well - behaved, while in the Reissner - Nordstr\o
m case they develop instabilities inside the horizon, near where the
repulsive effects of the charge dominate over those of the mass. In general,
whenever large enough repulsive effects in the gravitational background are
present, string instabilities develop. In De Sitter space, all the spatial
components exhibit instability. The infalling of the string to the black hole
singularity is like the motion of a particle in a potential
where depends on the spacetime
dimensions and string angular momentum, with for Schwarzschild and
for Reissner - Nordstr\o m black holes. For the
string ends trapped by the black hole singularity.Comment: 26pages, Plain Te
CLASSICAL SPLITTING OF FUNDAMENTAL STRINGS
We find exact solutions of the string equations of motion and constraints
describing the {\em classical}\ splitting of a string into two. We show that
for the same Cauchy data, the strings that split have {\bf smaller} action than
the string without splitting. This phenomenon is already present in flat
space-time. The mass, energy and momentum carried out by the strings are
computed. We show that the splitting solution describes a natural decay process
of one string of mass into two strings with a smaller total mass and some
kinetic energy. The standard non-splitting solution is contained as a
particular case. We also describe the splitting of a closed string in the
background of a singular gravitational plane wave, and show how the presence of
the strong gravitational field increases (and amplifies by an overall factor)
the negative difference between the action of the splitting and non-splitting
solutions.Comment: 27 pages, revtex
String propagation in four-dimensional dyonic black hole background
We study string propagation in an exact, four-dimensional dyonic black hole
background. The general solutions describing string configurations are obtained
by solving the string equations of motion and constraints. By using the
covariant formalism, we also investigate the propagation of physical
perturbations along the string in the given curved background.Comment: 19 pages, Tex (macro phyzzx is needed
Rigidly Rotating Strings in Stationary Spacetimes
In this paper we study the motion of a rigidly rotating Nambu-Goto test
string in a stationary axisymmetric background spacetime. As special examples
we consider the rigid rotation of strings in flat spacetime, where explicit
analytic solutions can be obtained, and in the Kerr spacetime where we find an
interesting new family of test string solutions. We present a detailed
classification of these solutions in the Kerr background.Comment: 19 pages, Latex, 9 figures, revised for publication in Classical and
Quantum Gravit
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