Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branes

The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their application is extended from ordinary harmonic models to a more general category of "harmonious" field models, with emphasis on cases in which the field is confined to a string or higher brane worldsheet, and for which the relevant internal symmetry group is non Abelian, so that the conditions for conservation of the corresponding charge currents become rather delicate, particularly when the symmetry is gauged. Attention is also given to the conditions for conservation of currents of a different kind -- representing surface fluxes of generalised momentum or energy -- associated with symmetries not of the internal target space but of the underlying spacetime background structure, including the metric and any relevant gauge field. For the corresponding current to be conserved the latter need not be manifestly invariant: preservation modulo a gauge adjustment will suffice. The simplest case is that of "strong" symmetry, meaning invariance under the action of an effective Lie derivative (an appropriately gauge adjusted modification of an ordinary Lie derivative). When the effective symmetry is of the more general "weak" kind, the kinetic part of the current is not conserved by itself but only after being supplemented by a suitable contribution from the background.Comment: 27 pages Latex (color

Poly-essential and general Hyperelastic World (brane) models

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model - the k-essential analogue of an ordinary polytropic fluid - is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio $w$ is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005: Micro and Macro Structures of Spacetim

Chaotic string-capture by black hole

We consider a macroscopic charge-current carrying (cosmic) string in the background of a Schwarzschild black hole. The string is taken to be circular and is allowed to oscillate and to propagate in the direction perpendicular to its plane (that is parallel to the equatorial plane of the black hole). Nurmerical investigations indicate that the system is non-integrable, but the interaction with the gravitational field of the black hole anyway gives rise to various qualitatively simple processes like "adiabatic capture" and "string transmutation".Comment: 13 pages Latex + 3 figures (not included), Nordita 93/55

Transonic Elastic Model for Wiggly Goto-Nambu String

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.Comment: 8 pages, plain TeX, no figure

The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics

The natural relativistic generalisation of Landau's two constituent superfluid theory can be formulated in terms of a Lagrangian $L$ that is given as a function of the entropy current 4-vector $s^\rho$ and the gradient $\nabla\varphi$ of the superfluid phase scalar. It is shown that in the ``cool" regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function $L(\vec s, \nabla\varphi)$ is given by an expression of the form $L=P-3\psi$ where $P$ represents the pressure as a function just of $\nabla\varphi$ in the (isotropic) cold limit. The entropy current dependent contribution $\psi$ represents the generalised pressure of the (non-isotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ``phonon" speed $c_P$ that is determined by the cold pressure function $P$.Comment: 26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 199

Quantum Ergoregion Instability

We have shown that, as in the case of black holes, an ergosphere itself with no event horizon inside can evaporate spontaneously, giving energy radiation to spatial infinity until the ergoregion disappears. However, the feature of his quantum ergoregion instability is very much different from black hole radiation. It is rather analogous to a laser amplification. This analysis is based on the canonical quantization of a neutral scalar field in the presence of unstable modes characterized by complex frequencies in a simple model for a rapidly rotating star.Comment: 10 pages, latex, one epsfig, to appear in the Proceedings of the APCTP Winter School on Duality of String Theory, Korea, Feb. 17-28, 1997; a brief version of gr-qc/9701040 with slightly different presentatio

Bonded joint and method

An improved joint is described for reducing the peak shear stress in adhesive bonds when adhesives are used to bond two materials which are in a lapped relationship and which differ in value of modulus of elasticity. An insert placed between the adhesive and one of the two materials acts to cushion the discontinuity of material stiffness thereby reducing the peak shear stress in the adhesive bond

Cold, warm, and composite (cool) cosmic string models

The dynamical behaviour of a cosmic string is strongly affected by any reduction of the effective string tension $T$ below the constant value $T=m^2$ say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu string model in terms of a fixed mass scale $m$ whose magnitude depends on that of the Higgs field responsible for the existence of the string. Such a reduction occurs in the standard "hot" cosmic string model in which the effect of thermal perturbations of a simple Goto Nambu model is expressed by the formula $T^2=m^2(m^2-2\pi\Theta^2/3)$, where $\Theta$ is the string temperature. A qualitatively similar though analytically more complicated tension reduction phenomenon occurs in "cold" conducting cosmic string models where the role of the temperature is played by an effective chemical potential $\mu$ that is constructed as the magnitude of the phase $\phi$ of a bosonic condensate of the kind whose existence was first proposed by Witten. The present article describes the construction and essential mechanical properties of a category of "warm" cosmic string models that are intermediate between these "hot" and "cold" extremes. These "warm" models are the string analogues of the standard Landau model for a 2-constituent finite temperature superfluid, and as such involve two independent currents interpretable as that of the entropy on one hand and that of the bosonic condensate on the other. It is surmised that the stationary (in particular ring) equilibrium states of such "warm" cosmic strings may be of cosmological significance.Comment: 31 pages, Tex preprint version of manuscript subsequently published (with editorial modifications) in Nuclear Physics

Regularisation of classical self interaction in strings

A general method of regularisation of classical self interaction in strings is extended from the electromagnetic case (for which it was originally developed) to the gravitation case, for which the result can also be represented as a renormalisation.Comment: 4 pages, Latex. Contribution to proceedings of 1997 Cargese A.S.I. ``Strings, branes, and dualities'', ed. L. Baulieu, P. Winde

Staticity Theorem for Higher Dimensional Generalized Einstein-Maxwell System

We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the topology of (n-2)-sphere we obtained the generalized first law of black hole thermodynamics. Supposing that a black hole evevt horizon comprisesw a bifurcation Killing horizon with a bifurcate surface we find that the solution is static in the exterior world, when the Killing timelike vector field is normal to the horizon and has vanishing electric or magnetic fields on static slices.Comment: 10 pages, REVTEX, to published in Phys.Rev. D1