630 research outputs found
R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars
We investigate properties of -mode instability in slowly rotating
relativistic polytropes. Inside the star slow rotation and low frequency
formalism that was mainly developed by Kojima is employed to study axial
oscillations restored by Coriolis force. At the stellar surface, in order to
take account of gravitational radiation reaction effect, we use a near-zone
boundary condition instead of the usually imposed boundary condition for
asymptotically flat spacetime. Due to the boundary condition, complex
frequencies whose imaginary part represents secular instability are obtained
for discrete -mode oscillations in some polytropic models. It is found that
such discrete -mode solutions can be obtained only for some restricted
polytropic models. Basic properties of the solutions are similar to those
obtained by imposing the boundary condition for asymptotically flat spacetime.
Our results suggest that existence of a continuous part of spectrum cannot be
avoided even when its frequency becomes complex due to the emission of
gravitational radiation.Comment: 10 pages, 4 figures, accepted for publlication in PR
The rotational modes of relativistic stars: Numerical results
We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure
Differential rotation of nonlinear r-modes
Differential rotation of r-modes is investigated within the nonlinear theory
up to second order in the mode amplitude in the case of a slowly-rotating,
Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the
linear r-mode, which represents differential rotation that produces large scale
drifts of fluid elements along stellar latitudes. This solution includes a
piece induced by first-order quantities and another one which is a pure
second-order effect. Since the latter is stratified on cylinders, it cannot
cancel differential rotation induced by first-order quantities, which is not
stratified on cylinders. It is shown that, unlikely the situation in the
linearized theory, r-modes do not preserve vorticity of fluid elements at
second-order. It is also shown that the physical angular momentum and energy of
the perturbation are, in general, different from the corresponding canonical
quantities.Comment: 9 pages, revtex4; section III revised, comments added in Introduction
and Conclusions, references updated; to appear in Phys. Rev.
Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
We use existence results for Jang's equation and marginally outer trapped
surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity.
In particular, our results show that any 2+1 initial data set, which obeys the
dominant energy condition with cosmological constant \Lambda \geq 0 and which
satisfies a mild asymptotic condition, must have trivial topology. Moreover,
any data set obeying these conditions cannot contain a MOTS. The asymptotic
condition involves a cutoff at a finite boundary at which a null mean convexity
condition is assumed to hold; this null mean convexity condition is satisfied
by all the standard asymptotic boundary conditions. The results presented here
strengthen various aspects of previous related results in the literature. These
results not only have implications for classical 2+1 gravity but also apply to
quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have
been combined to give a single proof, thereby circumventing an issue with the
second proof associated with potential blow-ups of solutions to Jang's
equation. To appear in Commun. Math. Phy
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
r-modes in Relativistic Superfluid Stars
We discuss the modal properties of the -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 . We find that the
basic properties of the -modes in a relativistic superfluid star are very
similar to those found for a Newtonian superfluid star. The -modes of a
relativistic superfluid star are split into two families, ordinary fluid-like
-modes (-mode) and superfluid-like -modes (-mode). The two
superfluids counter-move for the -modes, while they co-move for the
-modes. For the -modes, the quantity is
almost independent of the entrainment parameter , where and
are the azimuthal wave number and the oscillation frequency observed by an
inertial observer at spatial infinity, respectively. For the -modes, on
the other hand, almost linearly increases with increasing . It
is also found that the radiation driven instability due to the -modes is
much weaker than that of the -modes because the matter current associated
with the axial parity perturbations almost completely vanishes.Comment: 14 pages, 4 figures. To appear in Physical Review
RubiX: combining spatial resolutions for Bayesian inference of crossing fibers in diffusion MRI
The trade-off between signal-to-noise ratio (SNR) and spatial specificity governs the choice of spatial resolution in magnetic resonance imaging (MRI); diffusion-weighted (DW) MRI is no exception. Images of lower resolution have higher signal to noise ratio, but also more partial volume artifacts. We present a data-fusion approach for tackling this trade-off by combining DW MRI data acquired both at high and low spatial resolution. We combine all data into a single Bayesian model to estimate the underlying fiber patterns and diffusion parameters. The proposed model, therefore, combines the benefits of each acquisition. We show that fiber crossings at the highest spatial resolution can be inferred more robustly and accurately using such a model compared to a simpler model that operates only on high-resolution data, when both approaches are matched for acquisition time
Two physical characteristics of numerical apparent horizons
This article translates some recent results on quasilocal horizons into the
language of general relativity so as to make them more useful to
numerical relativists. In particular quantities are described which
characterize how quickly an apparent horizon is evolving and how close it is to
either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk
given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in
response to referees comments to improve clarity and fix typos. One reference
adde
Gravitational-wave astronomy: the high-frequency window
This contribution is divided in two parts. The first part provides a
text-book level introduction to gravitational radiation. The key concepts
required for a discussion of gravitational-wave physics are introduced. In
particular, the quadrupole formula is applied to the anticipated
``bread-and-butter'' source for detectors like LIGO, GEO600, EGO and TAMA300:
inspiralling compact binaries. The second part provides a brief review of high
frequency gravitational waves. In the frequency range above (say) 100Hz,
gravitational collapse, rotational instabilities and oscillations of the
remnant compact objects are potentially important sources of gravitational
waves. Significant and unique information concerning the various stages of
collapse, the evolution of protoneutron stars and the details of the
supranuclear equation of state of such objects can be drawn from careful study
of the gravitational-wave signal. As the amount of exciting physics one may be
able to study via the detections of gravitational waves from these sources is
truly inspiring, there is strong motivation for the development of future
generations of ground based detectors sensitive in the range from hundreds of
Hz to several kHz.Comment: 21 pages, 5 figures, Lectures presented at the 2nd Aegean Summer
School on the Early Universe, Syros, Greece, September 200
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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