16 research outputs found
Implications of the r-mode instability of rotating relativistic stars
Several recent surprises appear dramatically to have improved the likelihood
that the spin of rapidly rotating, newly formed neutron stars (and, possibly,
of old stars spun up by accretion) is limited by a nonaxisymmetric instability
driven by gravitational waves. Except for the earliest part of the spin-down,
the axial l=m=2 mode (an r-mode) dominates the instability, and the emitted
waves may be observable by detectors with the sensitivity of LIGO II. A review
of these hopeful results is followed by a discussion of constraints on the
instability set by dissipative mechanisms, including viscosity, nonlinear
saturation, and energy loss to a magnetic field driven by differential
rotation.Comment: 20 pages LaTeX2e (stylefile included), 6 eps figures. Review to
appear in the proceedings of the 9th Marcel Grossman Meeting, World
Scientific, ed. V. Gurzadyan, R. Jantzen, R. Ruffin
Gravitational-wave driven instability of rotating relativistic stars
A brief review of the stability of rotating relativistic stars is followed by
a more detailed discussion of recent work on an instability of r-modes, modes
of rotating stars that have axial parity in the slow-rotation limit. These
modes may dominate the spin-down of neutron stars that are rapidly rotating at
birth, and the gravitational waves they emit may be detectable.Comment: 14 pages PTPTeX v.1.0. Contribution to proceedings of the 1999 Yukawa
International Semina
A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
Numerical codes based on a direct implementation of the standard ADM
formulation of Einstein's equations have generally failed to provide long-term
stable and convergent evolutions of black hole spacetimes when excision is used
to remove the singularities. We show that, for the case of a single black hole
in spherical symmetry, it is possible to circumvent these problems by adding to
the evolution equations terms involving the constraints, thus adjusting the
standard ADM system. We investigate the effect that the choice of the lapse and
shift has on the stability properties of numerical simulations and thus on the
form of the added constraint term. To facilitate this task, we introduce the
concept of quasi well-posedness, a version of well-posedness suitable for
ADM-like systems involving second-order spatial derivatives.Comment: 20 pages, 9 figure
Differential rotation of the unstable nonlinear r-modes
At second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r-mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state
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