342 research outputs found
STATIONARY STRINGS AND 2-D BLACK HOLES
A general description of string excitations in stationary spacetimes is
developed. If a stationary string passes through the ergosphere of a
4-dimensional black hole, its world-sheet describes a 2-dimensional black (or
white) hole with horizon coinciding with the static limit of the 4-dimensional
black hole. Mathematical results for 2-dimensional black holes can therefore be
applied to physical objects (say) cosmic strings in the vicinity of Kerr black
holes. An immediate general result is that the string modes are thermally
excited. The string excitations are determined by a coupled system of scalar
field equations in the world-sheet metric. In the special case of excitations
propagating along a stationary string in the equatorial plane of the
Kerr-Newman black hole, they reduce to the -wave scalar field equations in
the 4-dimensional Reissner-Nordstr\"{o}m black hole. We briefly discuss
possible applications of our results to the black hole information puzzle.Comment: 13 pages, Late
Scattering of string-waves on black hole background
We consider the propagation of perturbations along an infinitely long
stationary open string in the background of a Schwarzschild black hole. The
equations of motion for the perturbations in the 2 transverse physical
directions are solved to second order in a weak field expansion. We then set up
a scattering formalism where an ingoing wave is partly transmitted and partly
reflected due to the interaction with the gravitational field of the black
hole. We finally calculate the reflection coefficient to third order in our
weak field expansion.Comment: 18 pages + 2 figures, Latex, Nordita-93/52
Weiss-approach to pair of coupled non-linear reaction-diffusion equations
We consider a pair of coupled non-linear partial differential equations
describing a biochemical model system. The Weiss-algorithm for the Painle\'{e}
test, that has been succesfully used in mathematical physics for the
KdV-equation, Burgers equation, the sine-Gordon equation etc., is applied, and
we find that the system possesses only the "conditional" Painlev\'{e} property.
We use the outcome of the analysis to construct an auto-B\"{a}cklund
transformation, and we find a variety of one and two-parameter families of
special solutions.Comment: 12 pages Latex, NORDITA-93/37
New Coherent String States and Minimal Uncertainty in WZWN Models
We study the properties of {\bf exact} (all level ) quantum coherent
states in the context of string theory on a group manifold (WZWN models).
Coherent states of WZWN models may help to solve the unitarity problem: Having
positive norm, they consistently describe the very massive string states
(otherwise excluded by the spin-level condition). These states can be
constructed by (at least) two alternative procedures: (i) as the exponential of
the creation operator on the ground state, and (ii) as eigenstates of the
annhilation operator. In the limit, all the known properties of
ordinary coherent states are recovered. States (i) and (ii) (which are
equivalent in the context of ordinary quantum mechanics and string theory in
flat spacetime) are not equivalent in the context of WZWN models. The set (i)
was constructed by these authors in a previous article. In this paper we
provide the construction of states (ii), we compare the two sets and discuss
their properties. We analyze the uncertainty relation, and show that states
(ii) satisfy automatically the {\it minimal uncertainty} condition for any ;
they are thus {\it quasiclassical}, in some sense more classical than states
(i) which only satisfy it in the limit. Modification to the
Heisenberg relation is given by , where is connected
to the string energy.Comment: More discussion on relation to previous work. More references added.
14 pages, Latex, no figure
Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions
The exact general evolution of circular strings in dimensional de
Sitter spacetime is described closely and completely in terms of elliptic
functions. The evolution depends on a constant parameter , related to the
string energy, and falls into three classes depending on whether
(oscillatory motion), (degenerated, hyperbolic motion) or
(unbounded motion). The novel feature here is that one single world-sheet
generically describes {\it infinitely many} (different and independent)
strings. The world-sheet time is an infinite-valued function of the
string physical time, each branch yields a different string. This has no
analogue in flat spacetime. We compute the string energy as a function of
the string proper size , and analyze it for the expanding and oscillating
strings. For expanding strings : even at ,
decreases for small and increases for large .
For an oscillating string , the average energy
over one oscillation period is expressed as a function of as a
complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under
request. LPTHE-PAR 93-5
Propagation of perturbations along strings
A covariant formalism for physical perturbations propagating along a string
in an arbitrary curved spacetime is developed. In the case of a stationary
string in a static background the propagation of the perturbations is described
by a wave-equation with a potential consisting of 2 terms: The first term
describing the time-dilation and the second is connected with the curvature of
space. As applications of the developed approach the propagation of
perturbations along a stationary string in Rindler, de Sitter, Schwarzschild
and Reissner-Nordstrom spacetimes are investigated.Comment: 18 pages, LaTeX, Nordita-93/17
Supertubes versus superconducting tubes
In this paper we show the relationship between cylindrical D2-branes and
cylindrical superconducting membranes described by a generic effective action
at the bosonic level. In the first case the extended objects considered, arose
as blown up type IIA superstrings to D2-branes, named supertubes. In the second
one, the cosmological objects arose from some sort of field theories. The
Dirac-Born-Infeld action describing supertubes is shown to be equivalent to the
generic effective action describing superconducting membranes via a special
transformation.Comment: Version with minor text changes with respect to the already publishe
On String Tunneling in Power Law Inflationary Universes
We consider the evolution of circular string loops in power law expanding
universes represented by a spatially flat Friedman-Robertson-Walker metric with
scale factor where is the cosmic time and . Our
main result is the existence of a "magic" power . In
spacetimes with a circular string expands either forever or to a
maximal radius and then contracts until it collapses into a point (black hole).
For , however, we find additional types of solutions. They include
configurations which contract from a positive initial radius to a minimal one
and then expand forever. Their existence we interpret as an indication for the
presence of a finite potential barrier. Equivalently the new solutions signal
string nucleation and tunneling, phenomena recently shown to occur in de Sitter
space.Comment: Latex, 9 pages + 4 figures (not included), NBI-HE-93-5
Open String Fluctuations in AdS with and without Torsion
The equations of motion and boundary conditions for the fluctuations around a
classical open string, in a curved space-time with torsion, are considered in
compact and world-sheet covariant form. The rigidly rotating open strings in
Anti de Sitter space with and without torsion are investigated in detail. By
carefully analyzing the tangential fluctuations at the boundary, we show
explicitly that the physical fluctuations (which at the boundary are
combinations of normal and tangential fluctuations) are finite, even though the
world-sheet is singular there. The divergent 2-curvature thus seems less
dangerous than expected, in these cases. The general formalism can be
straightforwardly used also to study the (bosonic part of the) fluctuations
around the closed strings, recently considered in connection with the AdS/CFT
duality, on AdS_5 \times S^5 and AdS_3 \times S^3 \times T^4.Comment: 19 pages, Late
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
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