arXiv subjects

Brandon Carter

Publications and source records attributed to Brandon Carter.

82 records · Page 5Linked to original sources

arXiv1997

Amalgamated Codazzi Raychaudhuri identity for foliation

It is shown how a pure background tensor formalism provides a concise but explicit and highly flexible machinery for the generalised curvature analysis of individual embedded surfaces and foliations such as arise in the theory of topological defects in cosmological and other physical contexts. The unified treatment provided here shows how the relevant extension of the Raychaudhuri identity is related to the correspondingly extended Codazzi identity.

hep-th↗

arXiv1997

Electromagnetic self interaction in strings

To facilitate the treatment of electromagnetic effects in applications such as dynamically perturbed vortons, this work employs a covariantly formulated string-source Green measure to obtain a coherent relativistic scheme for describing the self interaction of electromagnetic currents in string models of a very general kind, at leading order in the relevant field gradients, using a regularised gradient operator given by $\hat\nabla_ν=$ $\bar\nabla_ν+{1\over 2} K_ν$ where $\bar\nabla_ν$ is the usual tangential gradient operator and $K_ν$ is the extrinsic curvature vector.

hep-th↗

arXiv1996

Kalb-Ramond coupled vortex fibration model for relativistic superfluid dynamics

The macroscopic dynamics of a rotating superfluid deviates from that of a simple perfect fluid due to the effect of vorticity quantisation, which gives rise to a substructure of cosmic string type line defects that results in a local anisotropy whereby the effective average pressure in the direction of the vortex lines is reduced below its value in lateral directions. Whereas previous descriptions of this effect have been restricted to a non-relativistic framework that is adequate for the treatment of liquid helium in a laboratory context, the present work provides a fully relativistic description of the kind required for application to rotating neutron star models. To start with, the general category of vortex fibration models needed for this purpose is set up on the basis of a Kalb-Ramond type variational principle. The appropriate specification of the particular model to be chosen within this category will ultimately be governed by the conclusions of microscopic investigations that have not yet been completed, but the results available so far suggest that a uniquely simple kind of model with an elegant dilatonic formulation should be tentatively adopted as a provisional choice so long as there is no indication that a more complicated alternative is needed.

hep-th↗

arXiv1996

Dynamics of Cosmic Strings and other Brane models

The supporting worldsheet of a string, membrane, or other higher dimensional brane, is analysed in terms of its first, second, and third fundamental tensors, and its inner and outer curvature tensors. The dynamical equations governing the models appropriate for phenomena such as (superconducting) cosmic strings and cosmic domain walls are developed in a general framework (allowing for both electromagnetic and Kalb Ramond background coupling). It is shown how the surface stress momentum energy density tensor determines the propagation characteristics of small ``wiggle" perturbations of the worldsheet. Attention is then focussed on special features of strings (using the transonic model with tension T inversely proportional to the energy density U as a particularly important example). A quadratic Hamilton-Jacobi formulation is shown to govern equilibium states and other conservative string configurations sharing a symmetry of the (gravitational, electromagnetic, and Kalb-Ramond) background, including stable ring states that may be cosmologically important.

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arXiv1996

Avoidance of Collapse by Circular Current-Carrying Cosmic String Loops

Earlier attempts to calculate the nonlinear dynamical evolution of Witten type superconducting vacuum vortex defects relied on the use of approximate conducting string models that were too simple to take proper account of the effect of current saturation. This effect is however allowed for adequately in a newly developed class of rather more complicated, though still conveniently analytic, conducting string models. These more realistic models have recently been employed by Larsen and Axenides for investigating the collapse of circular string loops in the case for which angular momentum is absent. The present work extends this investigation to the generic case of circular string loops for which angular momentum is present, so that there will be a centrifugal potential barrier. This barrier will prevent collapse unless the initial conditions are such that the relevant current saturation limit is attained, in which case the string description of the vortex defect will break down, so that its subsequent fate is hard to foresee. On the other hand if saturation is avoided one would expect that the loop will eventually radiate away its excess energy and settle down into a vorton type equilibrium state.

hep-ph↗

arXiv1995

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 $s^ρ$ and the gradient $\nablaφ$ 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 $L(\vec s, \nablaφ)$ is given by an expression of the form $L=P-3ψ$ where $P$ represents the pressure as a function just of $\nablaφ$ in the (isotropic) cold limit. The entropy current dependent contribution $ψ$ 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 $P$.

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arXiv1995

Explicit Relativistic Vortex Solutions for Cool Two-Constituent Superfluid Dynamics

We give a class of explicit solutions for the stationary and cylindrically symmetric vortex configurations for a ``cool'' two-component superfluid (i.e. superfluid with an ideal gas of phonons). Each solution is characterized only by a set of (true) constants of integration. We then compute the effective asymptotic contribution of the vortex to the stress energy tensor by comparison with a uniform reference state without vortex.

hep-th↗

arXiv1994

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.

hep-th↗

arXiv1994

Supersonic String Model for Witten Vortices

A new cosmic string model specified by two independent mass parameters is introduced for the purpose of providing a realistic representation of the macroscopic dynamical behaviour of Witten type (superconducting) vortex defects of the vacuum. Unlike the self dual single mass parameter models previously used for this purpose, the new model successfully represents the effect of current saturation and the feature that wiggle propagation remains supersonic even in the weak current limit.

hep-ph↗

arXiv1994

Curvature Corrections to Dynamics of Domain Walls

The most usual procedure for deriving curvature corrections to effective actions for topological defects is subjected to a critical reappraisal. A logically unjustified step (leading to overdetermination) is identified and rectified, taking the standard domain wall case as an illustrative example. Using the appropriately corrected procedure, we obtain a new exact (analytic) expression for the corresponding effective action contribution of quadratic order in the wall width, in terms of the intrinsic Ricci scalar $R$ and the extrinsic curvature scalar $K$. The result is proportional to $cK^2-R$ with the coefficient given by $c\simeq 2$. The resulting form of the ensuing dynamical equations is obtained in terms of the second fundamental form and the Dalembertian of its trace, K. It is argued that this does not invalidate the physical conclusions obtained from the "zero rigidity" ansatz $c=0$ used in previous work.

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