A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars

General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic $\sigma - \omega$ mean field model for the nucleons and their interactions. In this context there are two notions of ``relativistic'': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly-rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.Comment: 16 pages, 5 figures, submitted to PR

Slowly Rotating General Relativistic Superfluid Neutron Stars with Relativistic Entrainment

Neutron stars that are cold enough should have two or more superfluids/supercondutors in their inner crusts and cores. The implication of superfluidity/superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect, i.e. the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modelling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic $\sigma$ - $\omega$ mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit.Comment: 30 pages, 10 figures, uses ReVTeX

Relativistic Two-stream Instability

We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow -- either across an interface or when two or more fluids interpenetrate -- and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the "free" (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (eg. no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.Comment: 15 pages, 2 eps-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

Relativistic Kinetics of Phonon Gas in Superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.Comment: 23 pages, Revtex fil

Neutron Stars in a Varying Speed of Light Theory

We study neutron stars in a varying speed of light (VSL) theory of gravity in which the local speed of light depends upon the value of a scalar field $\phi$. We find that the masses and radii of the stars are strongly dependent on the strength of the coupling between $\phi$ and the matter field and that for certain choices of coupling parameters, the maximum neutron star mass can be arbitrarily small. We also discuss the phenomenon of cosmological evolution of VSL stars (analogous to the gravitational evolution in scalar-tensor theories) and we derive a relation showing how the fractional change in the energy of a star is related to the change in the cosmological value of the scalar field.Comment: 15 pages, 2 figures. Added solutions with a more realistic equation of state. To be published in PR

Onset of inflation in inhomogeneous cosmology

We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe

r-modes in Relativistic Superfluid Stars

We discuss the modal properties of the $r$-modes of relativistic superfluid neutron stars, taking account of the entrainment effects between superfluids. In this paper, the neutron stars are assumed to be filled with neutron and proton superfluids and the strength of the entrainment effects between the superfluids are represented by a single parameter $\eta$. We find that the basic properties of the $r$-modes in a relativistic superfluid star are very similar to those found for a Newtonian superfluid star. The $r$-modes of a relativistic superfluid star are split into two families, ordinary fluid-like $r$-modes ($r^o$-mode) and superfluid-like $r$-modes ($r^s$-mode). The two superfluids counter-move for the $r^s$-modes, while they co-move for the $r^o$-modes. For the $r^o$-modes, the quantity $\kappa\equiv\sigma/\Omega+m$ is almost independent of the entrainment parameter $\eta$, where $m$ and $\sigma$ are the azimuthal wave number and the oscillation frequency observed by an inertial observer at spatial infinity, respectively. For the $r^s$-modes, on the other hand, $\kappa$ almost linearly increases with increasing $\eta$. It is also found that the radiation driven instability due to the $r^s$-modes is much weaker than that of the $r^o$-modes because the matter current associated with the axial parity perturbations almost completely vanishes.Comment: 14 pages, 4 figures. To appear in Physical Review

Long wavelength iteration of Einstein's equations near a spacetime singularity

We clarify the links between a recently developped long wavelength iteration scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general solution near a singularity and the antinewtonian scheme of Tomita's. We determine the regimes when the long wavelength or antinewtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity. When directly applicable we obtain the generic solution of the scheme at first iteration (third order in the gradients) for matter a perfect fluid. Specializing to spherical symmetry for simplicity and to clarify gauge issues, we then show how the metric behaves near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure

Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201