Arne L. Larsen

sinh-Gordon, cosh-Gordon, and Liouville equations for strings and multistrings in constant curvature spacetimes.

We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti{endash}de Sitter spacetimes (as well as in the 2+1 black hole anti{endash}de Sitter spacetime), {ital all} three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti{endash}de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. {copyright} {ital 1996 The American Physical Society.}

Chaotic scattering and capture of strings by a black hole

We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although it is a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition from order to chaos.

Null strings in Schwarzschild spacetime

The null string equations of motion and constraints in Schwarzschild spacetime are given. The solutions are those of the null geodesics of general relativity appended by a null string constraint in which the {open_quotes}constants of motion{close_quotes} 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 or tensile strings as compared to massless or 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. {copyright} {ital 1997} {ital The American Physical Society}

Runaway collapse of Witten vortex loops

We consider general properties of charged circular cosmic strings in a general family of worldsheet string models. We then specialize to a model recently proposed by Carter and Peter. This model was shown to give a good description of the features of the superconducting cosmic strings, originally discovered by Witten in a field theory. We derive an explicit expression for the potential determining the dynamics of the string and we present explicit expressions for the string tension and energy density, as a function of string-loop radius, in the locally preferred rest frame. We also obtain explicit expressions for the wiggle and woggle speeds (speeds of transverse and longitudinal perturbations, respectively). We show that the contraction of the uniformly charged string is essentially governed by the string tension (for large loop radius) and a finite Coulomb barrier (for small loop radius). We argue for the unobstructed contraction of a uniformly charged loop over the Coulombic barrier and its eventual collapse to a charged point. Finally, the implication of such an effect on the possible formation of naked singularities, in violation of the cosmic censorship hypothesis, is discussed.

Are higher order membranes stable in black hole spacetimes

We continue the study of the existence and stability of static spherical membrane configurations in curved spacetimes. We first consider higher order membranes described by a Lagrangian which, in addition to the Dirac term, includes a term proportional to the scalar curvature of the world volume {sup (3)}R. Notably, in this case, the equations of motion can be reduced to second order ones and an effective potential analysis can be made. The conditions for stability are then explicitly derived. We find a self-consistent static spherical membrane, determining the spacetime generated by the membrane itself. In this case we find, however, that the total energy of the membrane has to be negative, and no {ital stable} equilibrium can be achieved. We then generalize the discussion to a membrane described by a Lagrangian including all possible second derivative terms. We conclude the paper with some discussion on the generality of the results obtained. {copyright} {ital 1997} {ital The American Physical Society}

CHARGED COSMIC STRING NUCLEATION IN DE SITTER SPACE

We investigate aspects of the nucleation of charged circular cosmic strings in de Sitter space. By including the self-gravity for a single circular string loop we obtain the classical potential energy barrier and compute the quantum mechanical tunneling probability to horizon sizes in the semiclassical approximation. We also discuss the classical evolution of a pair of oppositely charged circular strings after their nucleation.

Cosmic string nucleation near the inflationary phase boundary

Abstract We investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.

On string tunneling in power law inflationary universes

Abstract 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 a(t) ∝ tp, where t is the cosmic time and p ⩾ 0. Our main result is the existence of a “magic” power p m = 3 + 2 2 . In spacetimes with p