923 research outputs found
Exact String Solutions in 2+1-Dimensional De Sitter Spacetime
Exact and explicit string solutions in de Sitter spacetime are found. (Here,
the string equations reduce to a sinh-Gordon model). A new feature without flat
spacetime analogy appears: starting with a single world-sheet, several (here
two) strings emerge. One string is stable and the other (unstable) grows as the
universe grows. Their invariant size and energy either grow as the expansion
factor or tend to constant. Moreover, strings can expand (contract) for large
(small) universe radius with a different rate than the universe.Comment: 11 pages, Phyzzx macropackage used, PAR-LPTHE 92/32. Revised version
with a new understanding of the previous result
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
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
QFT, String Temperature and the String Phase of De Sitter Space-time
The density of mass levels \rho(m) and the critical temperature for strings
in de Sitter space-time are found. QFT and string theory in de Sitter space are
compared. A `Dual'-transform is introduced which relates classical to quantum
string lengths, and more generally, QFT and string domains. Interestingly, the
string temperature in De Sitter space turns out to be the Dual transform of the
QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de
Sitter space is addressed selfconsistently in the framework of the `string
analogue' model (or thermodynamical approach), which is well suited to combine
QFT and string study.We find de Sitter space-time is a self-consistent solution
of the semiclassical Einstein equations in this framework. Two branches for the
scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a
quantum high curvature solution (+), enterely sustained by the strings. There
is a maximal value for the curvature R_{\max} due to the string back reaction.
Interestingly, our Dual relation manifests itself in the back reaction
solutions: the (-) branch is a classical phase for the geometry with intrinsic
temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy
phase for the geometry with temperature given by the intrinsic string de Sitter
temperature. 2 + 1 dimensions are considered, but conclusions hold generically
in D dimensions.Comment: LaTex, 24 pages, 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 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
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
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
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