31,945 research outputs found
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
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
A numerical study of the r-mode instability of rapidly rotating nascent neutron stars
The first results of numerical analysis of classical r-modes of {\it rapidly}
rotating compressible stellar models are reported. The full set of linear
perturbation equations of rotating stars in Newtonian gravity are numerically
solved without the slow rotation approximation. A critical curve of
gravitational wave emission induced instability which restricts the rotational
frequencies of hot young neutron stars is obtained. Taking the standard cooling
mechanisms of neutron stars into account, we also show the `evolutionary
curves' along which neutron stars are supposed to evolve as cooling and
spinning-down proceed. Rotational frequencies of stars suffering
from this instability decrease to around 100Hz when the standard cooling
mechanism of neutron stars is employed. This result confirms the results of
other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000
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
EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
This is the first of two papers on computing the self-force in a radiation
gauge for a particle moving in circular, equatorial orbit about a Kerr black
hole. In the EMRI (extreme-mass-ratio inspiral) framework, with mode-sum
renormalization, we compute the renormalized value of the quantity
, gauge-invariant under gauge transformations
generated by a helically symmetric gauge vector; and we find the related order
correction to the particle's angular velocity at fixed renormalized
redshift (and to its redshift at fixed angular velocity). The radiative part of
the perturbed metric is constructed from the Hertz potential which is extracted
from the Weyl scalar by an algebraic inversion\cite{sf2}. We then write the
spin-weighted spheroidal harmonics as a sum over spin-weighted spherical
harmonics and use mode-sum renormalization to find the renormalization
coefficients by matching a series in to the large- behavior of
the expression for . The
non-radiative parts of the perturbed metric associated with changes in mass and
angular momentum are calculated in the Kerr gauge
Effect of cessation of late-night landing noise on sleep electrophysiology in the home
Simultaneous measurements of noise exposure and sleep electrophysiology were made in homes before and after cessation of nighttime aircraft landing noise. Six people were tested, all of whom had been exposed to intense aircraft noise for at least two years. Noise measurements indicated a large reduction in the hourly noise level during nighttime hours, but no charge during the daytime hours. Sleep measures indicated no dramatic changes in sleep patterns either immediately after a marked change in nocturnal noise exposure or approximately a month thereafter. No strong relationship was observed between noise level and sleep disturbances over the range from 60 to 90 db(A)
Models of helically symmetric binary systems
Results from helically symmetric scalar field models and first results from a
convergent helically symmetric binary neutron star code are reported here;
these are models stationary in the rotating frame of a source with constant
angular velocity omega. In the scalar field models and the neutron star code,
helical symmetry leads to a system of mixed elliptic-hyperbolic character. The
scalar field models involve nonlinear terms that mimic nonlinear terms of the
Einstein equation. Convergence is strikingly different for different signs of
each nonlinear term; it is typically insensitive to the iterative method used;
and it improves with an outer boundary in the near zone. In the neutron star
code, one has no control on the sign of the source, and convergence has been
achieved only for an outer boundary less than approximately 1 wavelength from
the source or for a code that imposes helical symmetry only inside a near zone
of that size. The inaccuracy of helically symmetric solutions with appropriate
boundary conditions should be comparable to the inaccuracy of a waveless
formalism that neglects gravitational waves; and the (near zone) solutions we
obtain for waveless and helically symmetric BNS codes with the same boundary
conditions nearly coincide.Comment: 19 pages, 7 figures. Expanded version of article to be published in
Class. Quantum Grav. special issue on Numerical Relativit
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