39,881 research outputs found

### 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

### 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

### Recent developments in Vorton Theory

This article provides a concise overview of recent theoretical results
concerning the theory of vortons, which are defined to be (centrifugally
supported) equilibrium configurations of (current carrying) cosmic string
loops. Following a presentation of the results of work on the dynamical
evolution of small circular string loops, whose minimum energy states are the
simplest examples of vortons, recent order of magnitude estimates of the
cosmological density of vortons produced in various kinds of theoretical
scenario are briefly summarised.Comment: 6 pages Latex. Contribution to 1996 Cosmology Meeting, Peyresq,
Franc

### Renormalisation of gravitational self interaction for wiggly strings

It is shown that for any elastic string model with energy density $U$ and
tension $T$, the divergent contribution from gravitational self interaction can
be allowed for by an action renormalisation proportional to $(U-T)^2$. This
formula is applied to the important special case of a bare model of the
transonic type (characterised by a constant value of the product $UT$) that
represents the macroscopically averaged effect of shortwavelength wiggles on an
underlying microscopic model of the Nambu-Goto type (characterised by $U=T$).Comment: 11 pages, Latex; original 8 page version extended to include
estimates of relevant orders of magnitude. To be published in Physical
Review,

### The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin
sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode
perturbations when viscosity is present. The intuitive explanation is that
energy dissipation by viscosity can drive an unstable spheroid to a stable,
triaxial configuration of lower energy - a Jacobi ellipsoid. But what about
rapidly rotating compressible stars? Unlike incompressible stars, which contain
no internal energy and therefore immediately liberate all the energy dissipated
by viscosity, compressible stars have internal energy and can retain the
dissipated energy as internal heat. Now compressible stars that rotate
sufficiently rapidly and also manage to liberate this dissipated energy very
quickly are known to be unstable to bar-mode perturbations, like their
incompressible counterparts. But what is the situation for rapidly rotating
compressible stars that have very long cooling timescales, so that all the
energy dissipated by viscosity is retained as heat, whereby the total energy of
the star remains constant on a secular (viscous) evolution timescale? Are such
stars also unstable to the nonlinear growth of bar modes, or is the viscous
heating sufficient to cause them to expand, drive down the ratio of rotational
kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the
equatorial radius, and turn off the instability before it gets underway? If the
instability still arises in such stars, at what rotation rate do they become
unstable, and to what final state do they evolve? We provide answers to these
questions in the context of the compressible ellipsoid model for rotating
stars. The results should serve as useful guides for numerical simulations in
3+1 dimensions for rotating stars containing viscosity.Comment: Accepted for publication in ApJ 613, 1213-1220, 200

### 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

### Interaction of gravitational waves with an elastic solid medium

Contents. 1. Introduction. 2. Kinematics of a Material Medium: Material
Representation. 3. Kinematics of a Material Medium: Convected Differentials. 4.
Kinematics of a Perfect Elastic Medium. 5. Small Gravitational Perturbations of
an Elastic Medium.Comment: 14 pages TeX file of contrib. to proc. Gravitational Radiation, Les
Houches 1982, ed N. Deruelle, T. Piran, 455-464 (North Holland, Amsterdam,
1983

### 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

### 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

### Cosmic Vortons and Particle Physics Constraints

We investigate the cosmological consequences of particle physics theories
that admit stable loops of superconducting cosmic string - {\it vortons}.
General symmetry breaking schemes are considered, in which strings are formed
at one energy scale and subsequently become superconducting in a secondary
phase transition at what may be a considerably lower energy scale. We estimate
the abundances of the ensuing vortons, and thereby derive constraints on the
relevant particle physics models from cosmological observations. These
constraints significantly restrict the category of admissible Grand Unified
theories, but are quite compatible with recently proposed effects whereby
superconducting strings may have been formed close to the electroweak phase
transition.Comment: 33 pages, 2 figures, RevTe

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