4,078 research outputs found
Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --
It has been suggested that a naked singularity may be a good candidate for a
strong gravitational wave burster. The naked singularity occurs in the generic
collapse of an inhomogeneous dust ball. We study odd-parity mode of
gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi
space-time. The wave equation for gravitational waves are solved by numerical
integration using the single null coordinate. The result is that the naked
singularity is not a strong source of the odd-parity gravitational radiation
although the metric perturbation grows in the central region. Therefore, the
Cauchy horizon in this space-time would be marginally stable against odd-parity
perturbations.Comment: 14 pages, 7 figures, to be published in Prog. Theor. Phys. Final
version, with minor changes. Reference 13 adde
Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -
A naked singularity occurs in the generic collapse of an inhomogeneous dust
ball. We study the even-parity mode of gravitational waves from a naked
singularity of the Lema\^{\i}tre-Tolman-Bondi spacetime. The wave equations for
gravitational waves are solved by numerical integration using the single null
coordinate. The result implies that the metric perturbation grows when it
approaches the Cauchy horizon and diverges there, although the naked
singularity is not a strong source of even-parity gravitational radiation.
Therefore, the Cauchy horizon in this spacetime should be unstable with respect
to linear even-parity perturbations.Comment: 16 pages, 5 figures, errors and typos corrected, final versio
Physical Processes in Naked Singularity Formation
Gravitational collapse is one of the most fruitful subjects in gravitational
physics. It is well known that singularity formation is inevitable in complete
gravitational collapse. It was conjectured that such a singularity should be
hidden by horizons if it is formed from generic initial data with physically
reasonable matter fields. Many possible counterexamples to this conjecture have
been proposed over the past three decades, although none of them has proved to
be sufficiently generic. In these examples, there appears a singularity that is
not hidden by horizons. This singularity is called a `naked singularity.' The
appearance of a naked singularity represents the formation of an observable
high-curvature, strong-gravity region. In this paper we review examples of
naked singularity formation and recent progress in research of observable
physical processes - gravitational radiation and quantum particle creation -
from a forming naked singularity.Comment: 76 pages, 25 figure file
How Do Nonlinear Voids Affect Light Propagation ?
Propagation of light in a clumpy universe is examined. As an inhomogeneous
matter distribution, we take a spherical void surrounded by a dust shell where
the ``lost mass'' in the void is compensated by the shell. We study how the
angular-diameter distance behaves when such a structure exists. The
angular-diameter distance is calculated by integrating the Raychaudhuri
equation including the shear. An explicit expression for the junction condition
for the massive thin shell is calculated. We apply these results to a dust
shell embedded in a Friedmann universe and determine how the distance-redshift
relation is modified compared with that in the purely Friedmann universe. We
also study the distribution of distances in a universe filled with voids. We
show that the void-filled universe gives a larger distance than the FRW
universe by at if the size of the void is of the
Horizon radius.Comment: To appear in Prog. Theor. Phys. 10
Neumann problem for the Korteweg–de Vries equation
AbstractWe consider Neumann initial-boundary value problem for the Korteweg–de Vries equation on a half-line(0.1){ut+λuux+uxxx=0,t>0,x>0,u(x,0)=u0(x),x>0,ux(0,t)=0,t>0. We prove that if the initial data u0∈H10,214∩H21,72 and the norm ‖u0‖H10,214+‖u0‖H21,72⩽ε, where ε>0 is small enough Hps,k={f∈L2;‖f‖Hps,k=‖〈x〉k〈i∂x〉sf‖Lp<∞}, 〈x〉=1+x2 and λ∫0∞xu0(x)dx=λθ<0. Then there exists a unique solution u∈C([0,∞),H21,72)∩L2(0,∞;H22,3) of the initial-boundary value problem (0.1). Moreover there exists a constant C such that the solution has the following asymptoticsu(x,t)=Cθ(1+ηlogt)−1t−23Ai′(xt3)+O(ε2t−23(1+ηlogt)−65) for t→∞ uniformly with respect to x>0, where η=−9θλ∫0∞Ai′2(z)dz and Ai(q) is the Airy functionAi(q)=12πi∫−i∞i∞e−z3+zqdz=1πRe∫0∞e−iξ3+iξqdξ
Peierls Mechanism of the Metal-Insulator Transition in Ferromagnetic Hollandite K2Cr8O16
Synchrotron X-ray diffraction experiment shows that the metal-insulator
transition occurring in a ferromagnetic state of a hollandite
KCrO is accompanied by a structural distortion from the
tetragonal to monoclinic phase with a
supercell. Detailed electronic structure
calculations demonstrate that the metal-insulator transition is caused by a
Peierls instability in the quasi-one-dimensional column structure made of four
coupled Cr-O chains running in the -direction, leading to the formation of
tetramers of Cr ions below the transition temperature. This furnishes a rare
example of the Peierls transition of fully spin-polarized electron systems.Comment: Phys. Rev. Lett., in press, 5 pages, 3 figure
Langevin Analysis of Eternal Inflation
It has been widely claimed that inflation is generically eternal to the
future, even in models where the inflaton potential monotonically increases
away from its minimum. The idea is that quantum fluctuations allow the field to
jump uphill, thereby continually revitalizing the inflationary process in some
regions. In this paper we investigate a simple model of this process,
pertaining to inflation with a quartic potential, in which analytic progress
may be made. We calculate several quantities of interest, such as the expected
number of inflationary efolds, first without and then with various selection
effects. With no additional weighting, the stochastic noise has little impact
on the total number of inflationary efoldings even if the inflaton starts with
a Planckian energy density. A "rolling" volume factor, i.e. weighting in
proportion to the volume at that time, also leads to a monotonically decreasing
Hubble constant and hence no eternal inflation. We show how stronger selection
effects including a constraint on the initial and final states and weighting
with the final volume factor can lead to a picture similar to that usually
associated with eternal inflation.Comment: 22 pages, 2 figure
Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials
The object of the present study is the integrated density of states of a
quantum particle in multi-dimensional Euclidean space which is characterized by
a Schr\"odinger operator with a constant magnetic field and a random potential
which may be unbounded from above and from below. For an ergodic random
potential satisfying a simple moment condition, we give a detailed proof that
the infinite-volume limits of spatial eigenvalue concentrations of
finite-volume operators with different boundary conditions exist almost surely.
Since all these limits are shown to coincide with the expectation of the trace
of the spatially localized spectral family of the infinite-volume operator, the
integrated density of states is almost surely non-random and independent of the
chosen boundary condition. Our proof of the independence of the boundary
condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and
T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal.
{\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first
version of math-ph/0010013. For a revised version of the second part, see
math-ph/0105046. To appear in Reviews in Mathematical Physic
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