arXiv subjects

Brandon Carter

Publications and source records attributed to Brandon Carter.

At least 37 records · Page 2Linked to original sources

arXiv2007

The significance of numerical coincidences in nature

This is the first part of a survey whose ultimate purpose is to clarify the significance of the famous coincidence between the Hubble age of the universe and a certain combination of microphysical parameters. In this part the way is prepared by a discussion of the manner in which familiar local phenomena depend qualitatively, and in order of magnitude, quantitatively on the fundamental parameters of microphysics. In order to keep the account concise while remaining self contained, only the barest essentials of the standard nuclear physical and astrophysical calculations involved are given. Only six of the fundamental parameters play a dominant part, namely the coupling constants of the strong, electromagnetic, and gravitational forces, and the mass ratios of the proton, neutron, electron and pi-meson. Attention is drawn to the important consequences of three coincidental relationships between these parameters. It is shown that most of the principle limiting masses of astrophysics arise (in fundamental units) simply as the reciprocal of the gravitational fine structure constant, with relatively small adjustment factors. The dividing point between red dwarf and blue giant stars turns out to be an exception: this division occurs within the range of the main sequence stars only as a consequence of the rather exotic coincidence that the ninth power of the electromagnetic fine structure constant is roughly equal to the square root of the gravitational fine structure constant.

hep-th↗

arXiv2007

Mechanics of cosmic rings

In a flat background, simple non-conducting string loops have no strictly stationary equilibrium states, but for cosmic string loops of superconducting kind such ``vorton'' states will exist, with rotating circular configurations appropriately describable as ``cosmic rings'' (which may conceivably be a significant contributor to the material content of the universe) whose equilibrium is obtained for zero angular velocity of retrograde characteristics. Such a ``cosmic ring'' is characterised by its mass M and angular momentum J say, corresponding at a microscopic level to two independent quantum numbers, namely charge number C and a topological phase number N whose product determines the angular momentum, J=CN, while their ratio determines the local intrinsic state of the string, which may be qualitatively classified as being of ``electric'' or ``magnetic'' type depending on whether C/N is greater or less than a critical value dependent on the underlying theoretical model.

hep-th↗

arXiv2006

Relativistic mechanics of neutron superfluid in (magneto) elastic star crust

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure.

gr-qc↗

arXiv2006

Anthropic principle in cosmology

A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are contrasted with those that could be obtained from (less plausible) alternative prescriptions such as the vaguer and less restrictive ubiquity principle, or the more sterile and restrictive autocentric principle.

gr-qc↗

arXiv2006

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.

hep-th↗

arXiv2006

Half century of black-hole theory: from physicists' purgatory to mathematicians' paradise

Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a state of semiclandestine gestation until his demise. That turning point -- just half a century after Einstein's original foundation of relativity theory, and just half a century ago today -- can be considered to mark the birth of black hole theory as a subject of systematic development by physicists of a new and less inhibited generation, whose enthusastic investigations have revealed structures of unforeseen mathematical beauty, even though questions about the physical significance of the concomitant singularities remain controversial.

gr-qc↗

arXiv2006

Effect of entrainment on stress and pulsar glitches in neutron star crust

The build up of the stress whose relaxation is presumed to account for pulsar frequency glitches can be attributed to various mechanisms, of which the most efficient involve differential rotation of the neutron superfluid in the inner layers of the (magnetically braked) solid crust of a rotating neutron star. In such a case it is usually supposed that the stress is attributable to pinning of superfluid vortices to crust nuclei, but it has been suggested that, even if the pinning effect is too weak, a comparably large stress might still arise just from the deficit of centrifugal buoyancy in the slowed down crust. The present work is a re-examination that investigates the way such processes may be affected by considerations that were overlooked in the previous work -- notably uncertainties about the ``effective'' masses that have to be attributed to the ``free'' superfluid neutrons to allow for their entrainment by the ionic crust material. Though restricted to a Newtonian formulation, this analysis distinguishes more carefully than has been usual between true velocities, which are contravariantly vectorial, and so called ``superfluid velocities'' that are proportional to momenta, which are essentially covectorial, a technicality that is important when more than one independent current is involved. The results include a Proudman type theorem to the effect that the superfluid angular velocity must be constant on slightly deformed Taylor cylinders in the force free case, and it is shown how to construct a pair of integral constants of the motion that determine the solution for the pinned case assuming beta equilibrium.

astro-ph↗

arXiv2006

Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: II Macroscopic treatment

Phenomena such as pulsar frequency glitches are believed to be attributable to differential rotation of a current of ``free'' superfluid neutrons at densities above the ``drip'' threshold in the ionic crust of a neutron star. Such relative flow is shown to be locally describable by adaption of a canonical two fluid treatment that emphasizes the role of the momentum covectors constructed by differentiation of action with respect to the currents, with allowance for stratification whereby the ionic number current may be conserved even when the ionic charge number Z is altered by beta processes. It is demonstrated that the gauge freedom to make different choices of the chemical basis determining which neutrons are counted as ``free'' does not affect their ``superfluid'' momentum covector, which must locally have the form of a gradient (though it does affect the ``normal'' momentum covector characterising the protons and those neutrons that are considered to be ``confined'' in the nuclei). It is shown how the effect of ``entrainment'' (whereby the momentum directions deviate from those of the currents) is controlled by the (gauge independent) mobility coefficient K, estimated in recent microscopical quantum mechanical investigations, which suggest that the corresponding (gauge dependent) ``effective mass'' m* of the free neutrons can become very large in some layers. The relation between this treatment of the crust layers and related work (using different definitions of ``effective mass'') intended for the deeper core layers is discussed.

astro-ph↗

arXiv2006

Newtonian mechanics of neutron superfluid in elastic star crust

To account for pulsar frequency glitches, it is necessary to use a neutron star crust model allowing not only for neutron superfluidity but also for elastic solidity. These features have been treated separarately in previous treatments of crust matter, but are combined here in a unified treatment that is based on the use of a Lagrangian master functon, so that the coherence the system is ensured by the relevant Noether identities. As well as the model obtained directly from the variation principle, the same master function can provide other conservative alternatives, allowing in particular for the effect of perfect vortex pinning. It is also shown how such models can be generalised to allow for dissipative effects, including that of imperfect pinning, meaning vortex drag or creep.

astro-ph↗

arXiv2005

Effect of BCS pairing on entrainment in neutron superfluid current in neutron star crust

The relative current density $n^i$ of conduction neutrons in a neutron star crust beyond the neutron drip threshold can be expected to be related to the corresponding particle momentum covector $p_i$ by a linear relation of the form $n^i=K^{ij}p_j$ in terms of a physically well defined mobility tensor $K^{ij}$. This result is describable as an ``entrainment'' whose effect - wherever the crust lattice is isotropic - will simply be to change the ordinary neutron mass m to an effective mass $m_\star$ such that in terms of the relevant number density n of unconfined neutrons we shall have $K^{ij}=n/m_\starγ^{ij}$. In a preceding analysis based on an independent particle treatment using Bloch boundary conditions to obtain the distribution of energy $E_k$ and associated group velocity $v_k^i=\partial E_k/\partial\hbar k_i$ as a function of wavenumber $k_i$, it was shown that the mobility tensor would be given by $K^{ij}\propto\int d^3 k v_k^i v_k^jδ\{E_k-μ\}$, where $μ$ is the Fermi energy. Using the approach due to Bogoliubov, it is shown here that the effect of BCS pairing with an energy gap Δ_F and corresponding quasiparticle energy function \EE_k=\sqrt{(E_k-μ)^2+Δ_F^2}$ will just be to replace the Dirac distributional integrand by a smoother distribution : $K^{ij}\propto \int d^3 k v_k^i v_k^j Δ_F^2 /\EE^3_k$. It is also shown how the pairing condensation gives rise to superfluidity in the technical sense of providing (meta) stability against resistive perturbations for a current that is not too strong (its momentum $p_i$ must be small enough to give $2|p_i v_k^i|<\EE_k^2/|E_k-μ|$ for all modes). It is concluded that the prediction of a very large effective mass enhancement in the middle layers of the crust will not be significantly affected by the pairing mechanism.

astro-ph↗

arXiv2005

Covariant Newtonian and Relativistic dynamics of (magneto)-elastic solid model for neutron star crust

This work develops the dynamics of perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.

gr-qc↗

arXiv2005

Micro-Anthropic Principle for Quantum theory

Probabilistic models (developped by workers such as Boltzmann, on foundations due to pioneers such as Bayes) were commonly regarded merely as approximations to a deterministic reality before the roles were reversed by the quantum revolution (under the leadership of Heisenberg and Dirac) whereby it was the deterministic description that was reduced to the status of an approximation, while the role of the observer became particularly prominent. The concomitant problem of lack of objectivity in the original Copenhagen interpretation has not been satisfactorily resolved in newer approaches of the kind pioneered by Everett. The deficiency of such interpretations is attributable to failure to allow for the anthropic aspect of the problem, meaning {\it a priori} uncertainty about the identity of the observer. The required reconciliation of subjectivity with objectivity is achieved here by distinguishing the concept of an observer from that of a perceptor, whose chances of identification with a particular observer need to be prescribed by a suitable anthropic principle. It is proposed that this should be done by an entropy ansatz according to which the relevant micro-anthropic weighting is taken to be proportional to the logarithm of the relevant number of Everett type branch-channels.

quant-ph↗

arXiv2005

Frozen rigging model of the energy dominated universe

Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out into static lattice type configurations with energy contribution ultimately be provided by the membranes. It has been suggested by Bucher and Spergel that on scales large compared with the relevant (interstellar separation) distance characterising the relevant mesh length, such a system may behave as a rigidity - stabilised solid, having an approximately isotropic stress energy tensor with negative pressure, as given by a polytropic index $γ=w+1=1/3$. It has recently been shown that such a system can be rigid enough to be stable if the number of membranes meeting at a junction is even (though not if it is odd). Using as examples an approximately O(3) symmetric scalar field model that can provide an ``8 color'' (body centered) cubic lattice, and an approximate U(1)$\times$ U(1) model offering a disordered ``5 color'' lattice, it is argued that such a mechanism can account naturally for the observed dark energy dominance of the universe, without ad hoc assumptions, other than that the relevant symmetry breaking phase transition should have occurred somewhere about the Kev energy range.

hep-ph↗

arXiv2005

Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: simple microscopic models

In the inner crust of a neutron star, at densities above the ``drip'' threshold, unbound ``conduction'' neutrons can move freely past through the ionic lattice formed by the nuclei. The relative current density $n^i= n \bar v^i$ of such conduction neutrons will be related to the corresponding mean particle momentum $p_i$ by a proportionality relation of the form $n^i= {\cal K}p^i$ in terms of a physically well defined mobility coefficient $\cal K$ whose value in this context has not been calculated before. Using methods from ordinary solid state and nuclear physics, a simple quantum mechanical treatment based on the independent particle approximation, is used here to formulate $\cal K$ as the phase space integral of the relevant group velocity over the neutron Fermi surface. The result can be described as an ``entrainment'' that changes the ordinary neutron mass m to a macroscopic effective mass per neutron that will be given -- subject to adoption of a convention specifying the precise number density n of the neutrons that are considered to be ``free'' -- by $m_\star=n/{\cal K}$. The numerical evaluation of the mobility coefficient is carried out for nuclear configurations of the ``lasagna'' and ``spaghetti'' type that may be relevant at the base of the crust. Extrapolation to the middle layers of the inner crust leads to the unexpected prediction that $m_\star$ will become very large compared with m.

nucl-th↗

arXiv2004

Linearized self-forces for branes

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu--Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.

hep-th↗

arXiv2004

Mechanics and Equilibrium Geometry of Black Holes, Membranes, and Strings

This course is designed to give a mathematically coherent introduction to the classical thory of black holes and also of strings and membranes (which are like the horizon of a black hole in being examples of physical systems based on a dynamically evolving world sheet) giving particular attention given to the study of the geometry of their equilibrium states.

hep-th↗

arXiv2004

Covariant analysis of Newtonian multi-fluid models for neutron stars: III Transvective, viscous, and superfluid drag dissipation

As a follow up to articles dealing firstly with a convective variational formulation in a Milne-Cartan framework for non-dissipative multi fluid models, and secondly with various ensuing stress energy conservation laws and generalised virial theorems, this work continues a series showing how analytical procedures developed in the context of General Relativity can be usefully adapted for implementation in a purely Newtonian framework where they provide physical insights that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. The present article describes the 4-dimensionally covariant treatment of various dissipative mechanisms, including viscosity in non-superfluid constituents, superfluid vortex drag, ordinary resistivity (mutual friction) between relatively moving non-superfluid constituents, and the transvective dissipation that occurs when matter is transformed from one constituent to another due to chemical disequilibrium such as may be produced by meridional circulation in neutron stars. The corresponding non dissipative limit cases of vortex pinning, convection, and chemical equilibrium are also considered.

astro-ph↗

arXiv2004

Anthropic interpretation of quantum theory

The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the issue by the reintroduction of determinism at the global level of a ``state vector of the universe''. The present approach is based on the recognition that, like determinism, objective reality is an unrealistic objective. It is shown how an objective theory of an essentially subjective reality can be set up using an appropriately weighted probability measure on the relevant set of Hilbert subspaces. It is suggested that an entropy principle (superseding the weak anthropic principle) should be used to provide the weighting that is needed.

hep-th↗