3,366 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
Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves
We study the massless scalar field on asymptotically flat spacetimes with
closed timelike curves (CTC's), in which all future-directed CTC's traverse one
end of a handle (wormhole) and emerge from the other end at an earlier time.
For a class of static geometries of this type, and for smooth initial data with
all derivatives in on {\cI}^{-}, we prove existence of smooth solutions
which are regular at null and spatial infinity (have finite energy and finite
-norm) and have the given initial data on \cI^-. A restricted uniqueness
theorem is obtained, applying to solutions that fall off in time at any fixed
spatial position. For a complementary class of spacetimes in which CTC's are
confined to a compact region, we show that when solutions exist they are unique
in regions exterior to the CTC's. (We believe that more stringent uniqueness
theorems hold, and that the present limitations are our own.) An extension of
these results to Maxwell fields and massless spinor fields is sketched.
Finally, we discuss a conjecture that the Cauchy problem for free fields is
well defined in the presence of CTC's whenever the problem is well-posed in the
geometric-optics limit. We provide some evidence in support of this conjecture,
and we present counterexamples that show that neither existence nor uniqueness
is guaranteed under weaker conditions. In particular, both existence and
uniqueness can fail in smooth, asymptotically flat spacetimes with a compact
nonchronal region.Comment: 47 pages, Revtex, 7 figures (available upon request
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
Axial instability of rotating relativistic stars
Perturbations of rotating relativistic stars can be classified by their
behavior under parity. For axial perturbations (r-modes), initial data with
negative canonical energy is found with angular dependence for all
values of and for arbitrarily slow rotation. This implies instability
(or marginal stability) of such perturbations for rotating perfect fluids. This
low -instability is strikingly different from the instability to polar
perturbations, which sets in first for large values of . The timescale for
the axial instability appears, for small angular velocity , to be
proportional to a high power of . As in the case of polar modes,
viscosity will again presumably enforce stability except for hot, rapidly
rotating neutron stars. This work complements Andersson's numerical
investigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of
timescales is corrected and update
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