1,616 research outputs found
A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
We present a new variational framework for dissipative general relativistic
fluid dynamics. The model extends the convective variational principle for
multi-fluid systems to account for a range of dissipation channels. The key
ingredients in the construction are i) the use of a lower dimensional matter
space for each fluid component, and ii) an extended functional dependence for
the associated volume forms. In an effort to make the concepts clear, the
formalism is developed in steps with the model example of matter coupled to
heat considered at each level. Thus we discuss a model for heat flow, derive
the relativistic Navier-Stokes equations and discuss why the individual
dissipative stress tensors need not be spacetime symmetric. We argue that the
new formalism, which notably does not involve an expansion away from an assumed
equilibrium state, provides a conceptual breakthrough in this area of research
and provide an ambitious list of directions in which one may want to extend it
in the future. This involves an exciting set of problems, relating to both
applications and foundational issues.Comment: 21 pages RevTex, 3 pdf figures, matches the published version. arXiv
admin note: text overlap with arXiv:1107.1005 by other author
The nonlinear development of the relativistic two-stream instability
The two-stream instability has been mooted as an explanation for a range of
astrophysical applications from GRBs and pulsar glitches to cosmology. Using
the first nonlinear numerical simulations of relativistic multi-species
hydrodynamics we show that the onset and initial growth of the instability is
very well described by linear perturbation theory. In the later stages the
linear and nonlinear description match only qualitatively, and the instability
does not saturate even in the nonlinear case by purely ideal hydrodynamic
effects.Comment: 15 pages, 9 figure
Stationary structure of relativistic superfluid neutron stars
We describe recent progress in the numerical study of the structure of
rapidly rotating superfluid neutron star models in full general relativity. The
superfluid neutron star is described by a model of two interpenetrating and
interacting fluids, one representing the superfluid neutrons and the second
consisting of the remaining charged particles (protons, electrons, muons). We
consider general stationary configurations where the two fluids can have
different rotation rates around a common rotation axis. The previously
discovered existence of configurations with one fluid in a prolate shape is
confirmed.Comment: 5 pages, 2 figures. Conference proceedings for the 26th Spanish
Relativity Meeting (ERE 2002), Menorca, Spain, 22-24 Sept. 200
The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system
The inner crust of a mature neutron star is composed of an elastic lattice of
neutron-rich nuclei penetrated by free neutrons. These neutrons can flow
relative to the crust once the star cools below the superfluid transition
temperature. In order to model the dynamics of this system, which is relevant
for a range of problems from pulsar glitches to magnetar seismology and
continuous gravitational-wave emission from rotating deformed neutron stars, we
need to understand general relativistic Lagrangian perturbation theory for
elastic matter coupled to a superfluid component. This paper develops the
relevant formalism to the level required for astrophysical applications.Comment: 31 pages, double spacing, minor typos fixe
3+1 Approach to the Long Wavelength Iteration Scheme
Large-scale inhomogeneities and anisotropies are modeled using the Long
Wavelength Iteration Scheme. In this scheme solutions are obtained as
expansions in spatial gradients, which are taken to be small. It is shown that
the choice of foliation for spacetime can make the iteration scheme more
effective in two respects: (i) the shift vector can be chosen so as to dilute
the effect of anisotropy on the late-time value of the extrinsic curvature of
the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions
present in a similar calculation using the synchronous gauge vanish when the
spacelike hypersurfaces have extrinsic curvature with constant trace. We
furthermore verify the main conclusion of the synchronous gauge calculation
which is large-scale inhomogeneity decays if the matter--considered to be that
of a perfect-fluid with a barotropic equation of state--violates the
strong-energy condition. Finally, we obtain the solution for the lapse function
and discuss its late-time behaviour. It is found that the lapse function is
well-behaved when the matter violates the strong energy condition.Comment: 21 pages, TeX file, already publishe
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 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 - 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
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