4,291 research outputs found
Folded Strings Falling into a Black Hole
We find all the classical solutions (minimal surfaces) of open or closed
strings in {\it any} two dimensional curved spacetime. As examples we consider
the SL(2,R)/R two dimensional black hole, and any 4D black hole in the
Schwarzschild family, provided the motion is restricted to the time-radial
components. The solutions, which describe longitudinaly oscillating folded
strings (radial oscillations in 4D), must be given in lattice-like patches of
the worldsheet, and a transfer operation analogous to a transfer matrix
determines the future evolution. Then the swallowing of a string by a black
hole is analyzed. We find several new features that are not shared by particle
motions. The most surprizing effect is the tunneling of the string into the
bare singularity region that lies beyond the black hole that is classically
forbidden to particles.Comment: 28 pages plus 4 figures, LaTeX, USC-94/HEP-B
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 Quantization in Curved Spacetimes: Null String Approach
We study quantum strings in strong gravitational fields. The relevant small
parameter is , where is the curvature of the spacetime
and is the string tension. Within our systematic expansion we obtain to
zeroth order the null string (string with zero tension), while the first order
correction incorporates the string dynamics. We apply our formalism to quantum
null strings in de Sitter spacetime. After a reparametrization of the
world-sheet coordinates, the equations of motion are simplified. The quantum
algebra generated by the constraints is considered, ordering the momentum
operators to the right of the coordinate operators. No critical dimension
appears. It is anticipated however that the conformal anomaly will appear when
the first order corrections proportional to , are introduced.Comment: 6 pages, plain Tex, no figure
Cosmological evolution of warm dark matter fluctuations II: Solution from small to large scales and keV sterile neutrinos
We solve the cosmological evolution of warm dark matter (WDM) density
fluctuations with the Volterra integral equations of paper I. In the absence of
neutrinos, the anisotropic stress vanishes and the Volterra equations reduce to
a single integral equation. We solve numerically this equation both for DM
fermions decoupling at equilibrium and DM sterile neutrinos decoupling out of
equilibrium. We give the exact analytic solution for the density fluctuations
and gravitational potential at zero wavenumber. We compute the density contrast
as a function of the scale factor a for a wide range of wavenumbers k. At fixed
a, the density contrast grows with k for k
k_c, (k_c ~ 1.6/Mpc). The density contrast depends on k and a mainly through
the product k a exhibiting a self-similar behavior. Our numerical density
contrast for small k gently approaches our analytic solution for k = 0. For
fixed k < 1/(60 kpc), the density contrast generically grows with a while for k
> 1/(60 kpc) it exhibits oscillations since the RD era which become stronger as
k grows. We compute the transfer function of the density contrast for thermal
fermions and for sterile neutrinos in: a) the Dodelson-Widrow (DW) model and b)
in a model with sterile neutrinos produced by a scalar particle decay. The
transfer function grows with k for small k and then decreases after reaching a
maximum at k = k_c reflecting the time evolution of the density contrast. The
integral kernels in the Volterra equations are nonlocal in time and their
falloff determine the memory of the past evolution since decoupling. This
falloff is faster when DM decouples at equilibrium than when it decouples out
of equilibrium. Although neutrinos and photons can be neglected in the MD era,
they contribute in the MD era through their memory from the RD era.Comment: 27 pages, 6 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
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
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.
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