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$^2$) (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

Quasi-elastic peak lineshapes in adsorbate diffusion on nearly flat surfaces at low coverages: the motional narrowing effect in Xe on Pt(111)

Quasi-elastic helium atom scattering measurements have provided clear evidence for a two-dimensional free gas of Xe atoms on Pt(111) at low coverages. Increasing the friction due to the surface, a gradual change of the shape of the quasi-elastic peak is predicted and analyzed for this system in terms of the so-called motional narrowing effect. The type of analysis presented here for the quasi-elastic peak should be prior to any deconvolution procedure carried out in order to better extract information from the process, e.g. diffusion coefficients and jump distributions. Moreover, this analysis also provides conditions for the free gas regime different than those reported earlier.Comment: 12 pages, 4 figures (revised version

Exact String Solutions in Nontrivial Backgrounds

We show how the classical string dynamics in $D$-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 $D1$-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.

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

Boundaries in the Moyal plane

We study the oscillations of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. The space of quantum fluctuations of the field is finite dimensional and displays the rotational and parity symmetry of the disc. We perform a numerical evaluation of the (finite) Casimir energy and obtain similar results as for the fuzzy sphere and torus.Comment: 19 pages, 6 figures. Replaced by published versio

Line Shape Broadening in Surface Diffusion of Interacting Adsorbates with Quasielastic He Atom Scattering

The experimental line shape broadening observed in adsorbate diffusion on metal surfaces with increasing coverage is usually related to the nature of the adsorbate-adsorbate interaction. Here we show that this broadening can also be understood in terms of a fully stochastic model just considering two noise sources: (i) a Gaussian white noise accounting for the surface friction, and (ii) a shot noise replacing the physical adsorbate-adsorbate interaction potential. Furthermore, contrary to what could be expected, for relatively weak adsorbate-substrate interactions the opposite effect is predicted: line shapes get narrower with increasing coverage.Comment: 4 pages, 2 figures (slightly revised version

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 $X^0 \to 0$ and $X^0 \to \infty$ and we plot the numerical solution for all times. Right after the big bang ($X^0 = 0$), the string energy decreasess as $R(X^0)^{-1}$ and the string size grows as $R(X^0)$ for $0 1$. Very soon [ $X^0 \sim 1$] , 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

Optimal streaks in a Falkner-Skan boundary layer

This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations around the Falkner-Skan base flow. Based on an asymptotic analysis of this system near the free stream and the leading edge singularity, we show that for acute wedge semi-angle, all solutions converge after a streamwise transient to a single streamwise-growing solution of the linearized equations, whose initial condition near the leading edge is given by an eigenvalue problem first formulated in this context by Tumin (2001). Such a solution may be regarded as a streamwise evolving most unstable streaky mode, in analogy with the usual eigenmodes in strictly parallel flows, and shows an approximate self-similarity, which was partially known and is completed in this paper. An important consequence of this result is that the optimization procedure based on the adjoint equations heretofore used to define optimal streaks is not necessary. Instead, a simple low-dimensional optimization process is proposed and used to obtain optimal streaks. Comparison with previous results by Tumin and Ashpis (2003) shows an excellent agreement. The unstable streaky mode exhibits transient growth if the wedge semi-angle is smaller than a critical value that is slightly larger than $\pi/6$, and decays otherwise. Thus the cases of right and obtuse wedge semi-angles exhibit less practical interest, but they show a qualitatively different behavior, which is briefly described to complete the analysis

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

Null Strings in Schwarzschild Spacetime

The null string equations of motion and constraints in the Schwarzschild spacetime are given. The solutions are those of the null geodesics of General Relativity appended by a null string constraint in which the "constants of motion" depend on the world-sheet spatial coordinate. Because of the extended nature of a string, the physical interpretation of the solutions is completely different from the point particle case. In particular, a null string is generally not propagating in a plane through the origin, although each of its individual points is. Some special solutions are obtained and their physical interpretation is given. Especially, the solution for a null string with a constant radial coordinate $r$ moving vertically from the south pole to the north pole around the photon sphere, is presented. A general discussion of classical null/tensile strings as compared to massless/massive particles is given. For instance, tensile circular solutions with a constant radial coordinate $r$ do not exist at all. The results are discussed in relation to the previous literature on the subject.Comment: 16 pages, REVTEX, no figure