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Brandon Carter

Publications and source records attributed to Brandon Carter.

At least 55 records · Page 3Linked to original sources
arXiv2003

Covariant analysis of Newtonian multi-fluid models for neutron stars: I Milne-Cartan structure and variational formulation

This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. After an introductory presentation of the relevant Milne spacetime structure and the associated Cartan connection, the essential principles are illustrated by application to the variational formulation of simple barotropic perfect fluid models. This variational treatment is then extended to conservative multiconstituent self gravitating fluid models of the more general kind that is needed for treating the effects of superfluidity in neutron stars.

astro-ph↗
arXiv2003

Covariant analysis of Newtonian multi-fluid models for neutron stars: II Stress - energy tensors and virial theorems

The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding article of this series is developed by construction of the relevant 4-dimensional stress energy tensor whose conservation in the non-dissipative variational case is shown to be interpretable as a Noether identity of the Milne spacetime structure. The formalism is illustrated by the application to homogeneously expanding cosmological models, for which appropriately generalised local Bernouilli constants are constructed. Another application is to the Iordanski type generalisation of the Joukowski formula for the Magnus force on a vortex. Finally, at a global level, a new (formally simpler but more generally applicable) version of the ``virial theorem'' is obtained for multiconsituent -- neutron or other -- fluid star models as a special case within an extensive category of formulae whereby the time evolution of variously weighted mass moment integrals is determined by corresponding space integrals of stress tensor components, with the implication that all such stress integrals must vanish for any stationary equilibrium configuration.

astro-ph↗
arXiv2003

Dynamical instability criterion for circular (vorton) string loops

Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium (i.e. vorton) state of a closed string loop it is shown that the fundamental axisymmetric ($n=0$) and lowest order ($n=1$) nonaxisymmetric perturbation modes can never be unstable. However, stability for modes of higher order ($n\geq 2$) is found to be non-trivially dependent on the values of the characteristic propagation velocity, $c$ say, of longitudinal perturbations and of the corresponding extrinsic perturbation velocity, $v$ say. For each mode number the criterion for instability is the existence of nonreal roots for a certain cubic eigenvalue equation for the corresponding mode frequency. A very simple sufficient but not necessary condition for reality of the roots and therefore absence of instability is that the characteristic velocity ratio, $c/v$ be greater than or equal to unity. Closer examination of the low velocity (experimentally accessible) nonrelativistic regime shows that in that limit the criterion for instability is just that the dimensionless characteristic ratio $c/v$ be less than a critical value $χ_c$ whose numerical value is approximately $1\over 2$. In the relativistic regime that is relevant to superconducting cosmic strings the situation is rather delicate, calling for more detailed investigation that is postponed for future work.

hep-th↗
arXiv2003

Symplectic Structure in Brane Mechanics

This article treats the generalisation to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developped by Witten, Zuckerman and others in the context of field theory. After a general presentation, including a review of the relationships between the various (Lagrangian, Eulerian and other) relevant kinds of variation, the procedure is illustrated by application to the particularly simple case of branes of the Dirac-Goto-Nambu type, in which internal fields are absent.

hep-th↗
arXiv2002

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 $T^2=m^2(m^2-2πΘ^2/3)$, where $Θ$ 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 $μ$ that is constructed as the magnitude of the phase $ϕ$ 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.

hep-ph↗
arXiv2002

Energy dominance and the Hawking Ellis vacuum conservation theorem

At a time when uninhibited speculation about negative tension -- and by implication negative mass density -- world branes has become commonplace, it seems worthwhile to call attention to the risk involved in sacrificing traditional energy positivity postulates such as are required for the classical vacuum stability theorem of Hawking and Ellis. As well as recapitulating the technical content of this reassuring (when applicable) theorem, the present article provides a new, rather more economical proof.

gr-qc↗
arXiv2002

Gradient formula for linearly self-interacting branes

The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case) or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension.

hep-th↗
arXiv2002

Microwave Background Constraints on Decaying Defects

Embedded defects are predicted in a host of particle physics theories, in particular in the standard electroweak theory. They can be stabilized by interactions with the cosmological plasma, but will decay once the plasma falls out of equilibrium, emitting a substantial fraction of non-thermal photons. If the decay happens after a redshift of about $10^6$, these photons will give rise to spectral distortions of the Cosmic Microwave Background, which leads to strong constraints on the underlying particle physics theory. Such constraints apply to any model with decaying defects, and in particular to theories predicting decaying vortons, thereby leading to constraints stronger than the dark matter limit.

hep-ph↗
arXiv2002

Thermal Stabilisation of Superconducting Sigma Strings and their Drum Vortons

We discuss various issues related to stabilized embedded strings in a thermal background. In particular, we demonstrate that such strings will generically become superconducting at moderately low temperatures, thus enhancing their stability. We then present a new class of defects - drum vortons - which arise when a small symmetry breaking term is added to the potential. We display these points within the context of the O(4) sigma model, relevant for hadrodynamics below the QCD scale. This model admits `embedded defects' (topological defect configurations of a simpler - in this case O(2) symmetric - model obtained by imposing an embedding constraint) that are unstable in the full model at zero temperature, but that can be stabilised (by electromagnetic coupling to photons) in a thermal gas at moderately high termperatures. It is shown here that below the embedded defect stabilisation threshold, there will still be stabilized cosmic string defects. However, they will not be of the symmetric embedded vortex type, but of an `asymmetric' vortex type, and are automatically superconducting. In the presence of weak symmetry breaking terms, such as arise naturally when using the O(4) model for hadrodynamics, the strings become the boundary of a new kind of cosmic sigma membrane, with tension given by the pion mass. The string current would then make it possible for a loop to attain a (classically) stable equilibrium state that differs from an ``ordinary'' vorton state by the presence of a sigma membrane stretched across it in a drum like configuration. Such defects will however be entirely destabilised if the symmetry breaking is too strong, as is found to be the case -- due to the rather large value of the pion mass -- in the hadronic application of the O(4) sigma model.

hep-ph↗
arXiv2001

Simulated gravity without true gravity in asymmetric brane-world scenarios

This article investigates asymmetric brane-world scenarios in the limit when the bulk gravity is negligible. We show that, even when true self gravity is negligible, local mass concentrations will be subject to a mutual attraction force which simulates the effect of Newtonian gravity in the non-relativistic limit. Cosmological and also post-Newtonian constraints are examined.

gr-qc↗
arXiv2001

Quasi gravity in branes

In contrast with pseudo-gravitational effects that are mathematically analogous but physically quite distinct from gravity, this presentation deals with a kind of quasi-gravitational effect that can act in an asymmetrically moving brane worldsheet in a manner that approximates (and in a crude analysis might be physically indistinguishable from) the effect that would arise from genuine gravitation, of ordinary Newtonian type in non-relativistic applications, and of scalar - tensor (Jordan - Brans - Dicke rather than pure Einstein) type in relativistic applications.

hep-th↗
arXiv2001

Einstein equations for an asymmetric brane-world

We consider a brane-world of co-dimension one without the reflection symmetry that is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codacci equations, we derive the effective Einstein equations by relating the local curvature to the matter on the brane in the case when its bare tension is much larger than the localized matter, and hence show that Einstein gravity is a natural consequence of such models in the weak field limit. We find agreement with the recently derived cosmological case, which can be solved exactly, and point out that such models can be realized naturally in the case where there is a minimally coupled form field in the bulk.

hep-th↗
arXiv2001

Essentials of Classical Brane Dynamics

This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation in an ordinary 4 dimensional spacetime background. This category also includes ``brane world'' models that treat the observed universe as a 3-brane in 5 or higher dimensional background. The first sections are concerned with purely kinematic aspects: it is shown how, to second differential order, the geometry (and in particular the inner and outer curvature) of a brane worldsheet of arbitrary dimension is describable in terms of the first, second, and third fundamental tensor. The later sections show how -- to lowest order in the thin limit -- the evolution of such a brane worldsheet will always be governed by a simple tensorial equation of motion whose left hand side is the contraction of the relevant surface stress tensor $ bar T^{μν}$ with the (geometrically defined) second fundamental tensor $K_{μν}{^ρ}$, while the right hand side will simply vanish in the case of free motion and will otherwise be just the orthogonal projection of any external force density that may happen to act on the brane.

gr-qc↗
arXiv2001

Reflection symmetry breaking scenarios with minimal gauge form coupling in brane world cosmology

This article synthesises and extends recent work on the cosmological consequences of dropping the usual Z_2 reflection symmetry postulate in brane world scenarios. It is observed that for a cosmological model of homogeneous isotropic type, the relevant generalised Birkhoff theorem establishing staticity of the external vacuum in the maximally symmetric ``bulk'' outside a freely moving world brane will remain valid for the case of motion that is forced by minimal (generalised Wess Zumino type) coupling to an external antisymmetric gauge field provided its kinetic action contribution has the usual homogeneous quadratic form. This means that the geometry on each side of the brane worldsheet will still be of the generalised Schwarzschild anti de Sitter type. The usual first integrated Friedmann equation for the Hubble expansion rate can thereby be straightforwardly generalised by inclusion of new terms involving 2 extra parameters respectively measuring the strength of the gauge coupling and the degree of deviation from reflection symmetry. Some conceivable phenomenological implications are briefly outlined, and corresponding limitations are derived for possible values of relevant parameters.

gr-qc↗
arXiv2001

Relativistic solution of Iordanskii problem in multi-constituent superfluid mechanics

Flow past a line vortex in a simple perfect fluid or superfluid gives rise to a transverse Magnus force that is given by the well known Joukowski lift formula. The problem of generalising this to multiconstituent superfluid models has been controversial since it was originally posed by the work of Iordanski in the context of the Landau 2-constituent model for He-4 at finite temperature. The present work deals not just with this particular case but with the generic category of perfect multiconstituent models including the kind proposed for a mixture of He-4 and He-3 by Andreev and Bashkin. It is shown here (using a relativistic approach) that each constituent will provide a contribution proportional to the product of the corresponding momentum circulation integral with the associated asymptotic current density.

cond-mat↗
arXiv2001

Relativistic superfluid models for rotating neutron stars

This article starts by providing an introductory overview of the theoretical mechanics of rotating neutron stars as developped to account for the frequency variations, and particularly the discontinuous glitches, observed in pulsars. The theory suggests, and the observations seem to confirm, that an essential role is played by the interaction between the solid crust and inner layers whose superfluid nature allows them to rotate independently. However many significant details remain to be clarified, even in much studied cases such as the Crab and Vela. The second part of this article is more technical, concentrating on just one of the many physical aspects that needs further development, namely the provision of a satisfactorily relativistic (local but not microscopic) treatment of the effects of the neutron superfluidity that is involved.

astro-ph↗
arXiv2000

Superconducting Superfluids in Neutron Stars

For treatment of the layers below the crust of a neutron star it is useful to employ a relativistic model involving three independently moving constituents, representing superfluid neutrons, superfluid protons, and degenerate negatively charged leptons. A Kalb Ramond type formulation is used here to develop such a model for the specific purpose of application at the semi macroscopic level characterised by lengthscales that are long compared with the separation between the highly localised and densely packed proton vortices of the Abrikosov type lattice that carries the main part of the magnetic flux, but that are short compared with the separation between the neutron vortices.

astro-ph↗