3,291 research outputs found
The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity
The coupled equations for the scalar modes of the linearized Einstein
equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1
wave equation with a potential , on a field . For smooth metric
perturbations is singular at , the
mode harmonic number, and has a second order pole at . This is
irrelevant to the black hole exterior stability problem, where , and
, but it introduces a non trivial problem in the naked singular case
where , and the singularity appears in the relevant range of
. We solve this problem by developing a new approach to the evolution of the
even mode, based on a {\em new gauge invariant function}, -related
to by an intertwiner operator- that is a regular function of the
metric perturbation {\em for any value of }. This allows to address the
issue of evolution of gravitational perturbations in this non globally
hyperbolic background, and to complete the proof of the linear instability of
the Schwarzschild naked singularity, by showing that a previously found
unstable mode is excitable by generic initial data. This is further illustrated
by numerically solving the linearized equations for suitably chosen initial
data.Comment: typos corrected, references adde
Naked Singularity and Thunderbolt
We consider quantum theoretical effects of the sudden change of the boundary
conditions which mimics the occurrence of naked singularities. For a simple
demonstration, we study a massless scalar field in -dimensional
Minkowski spacetime with finite spatial interval. We calculate the vacuum
expectation value of the energy-momentum tensor and explicitly show that
singular wave or {\em thunderbolt} appears along the Cauchy horizon. The
thunderbolt possibly destroys the Cauchy horizon if its backreaction on the
geometry is taken into account, leading to quantum restoration of the global
hyperbolicity. The result of the present work may also apply to the situation
that a closed string freely oscillating is traveling to a brane and changes
itself to an open string pinned-down by the ends satisfying the Dirichlet
boundary conditions on the brane.Comment: 12 pages, 1 figure, references added, to appear in Phys. Rev.
Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes
Classically, the dynamics in a non-globally hyperbolic spacetime is ill
posed. Previously, a prescription was given for defining dynamics in static
spacetimes in terms of a second order operator acting on a Hilbert space
defined on static slices. The present work extends this result by giving a
similar prescription for defining dynamics in stationary spacetimes obeying
certain mild assumptions. The prescription is defined in terms of a first order
operator acting on a different Hilbert space from the one used in the static
prescription. It preserves the important properties of the earlier one: the
formal solution agrees with the Cauchy evolution within the domain of
dependence, and smooth data of compact support always give rise to smooth
solutions. In the static case, the first order formalism agrees with second
order formalism (using specifically the Friedrichs extension). Applications to
field quantization are also discussed.Comment: 18 pages, 1 figure, AMSLaTeX; v2: expanded discussion of field
quantization, new Proposition 3.1, revised Theorem 4.2, corrected typos, and
updated reference
Black-Hole Bombs and Photon-Mass Bounds
Generic extensions of the standard model predict the existence of ultralight
bosonic degrees of freedom. Several ongoing experiments are aimed at detecting
these particles or constraining their mass range. Here we show that massive
vector fields around rotating black holes can give rise to a strong
superradiant instability which extracts angular momentum from the hole. The
observation of supermassive spinning black holes imposes limits on this
mechanism. We show that current supermassive black hole spin estimates provide
the tightest upper limits on the mass of the photon (mv<4x10^{-20} eV according
to our most conservative estimate), and that spin measurements for the largest
known supermassive black holes could further lower this bound to mv<10^{-22}
eV. Our analysis relies on a novel framework to study perturbations of rotating
Kerr black holes in the slow-rotation regime, that we developed up to second
order in rotation, and that can be extended to other spacetime metrics and
other theories.Comment: 5 pages, 2 figures. References added. Matches published versio
Phase transitions and iron-ordered moment form factor in LaFeAsO
Elastic neutron scattering studies of an optimized LaFeAsO single crystal
reveal that upon cooling, an onset of the tetragonal (T)-to-orthorhombic (O)
structural transition occurs at K, and it exhibits a
sharp transition at K. We argue that in the
temperature range to , T and O structures may
dynamically coexist possibly due to nematic spin correlations recently proposed
for the iron pnictides, and we attribute to the formation of
long-range O domains from the finite local precursors. The antiferromagnetic
structure emerges at K, with the iron moment
direction along the O \emph{a} axis. We extract the iron magnetic form factor
and use the tabulated of Fe, Fe and Fe to
obtain a magnetic moment size of 0.8 at 9.5 K.Comment: 7 pages, 6 figures, 3 table
D-branes in the WZW model
It is stated in the literature that D-branes in the WZW-model associated with
the gluing condition J = - \bar{J} along the boundary correspond to branes
filling out the whole group volume. We show instead that the end-points of open
strings are rather bound to stay on `integer' conjugacy classes. In the case of
SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and
two D particles sitting at the points e and -e.Comment: 2 pages, LaTe
Spacetime Fermions in Light-cone Gauge Superstring Field Theory and Dimensional Regularization
We consider the dimensional regularization of the light-cone gauge type II
superstring field theories in the NSR formalism. In the previous work, we have
calculated the tree-level amplitudes with external lines in the (NS,NS) sector
using the regularization and shown that the desired results are obtained
without introducing contact term interactions. In this work, we study the
tree-level amplitudes with external lines in the Ramond sector. In order to
deal with them, we propose a worldsheet theory to be used instead of that for
the naive dimensional regularization. With the worldsheet theory, we regularize
and define the tree-level amplitudes by analytic continuation. We show that the
results coincide with those of the first quantized formulation.Comment: 28 pages, 5 figures; v2: more details of our manipulations in
subsection 3.2 added, figures and references added; v3: clarifications adde
Two-dimensional cellular automaton model of traffic flow with open boundaries
A two-dimensional cellular automaton model of traffic flow with open
boundaries are investigated by computer simulations. The outflow of cars from
the system and the average velocity are investigated. The time sequences of the
outflow and average velocity have flicker noises in a jamming phase. The low
density behavior are discussed with simple jam-free approximation.Comment: 14 pages, Phys. Rev. E in press, PostScript figures available at
ftp://hirose.ai.is.saga-u.ac.jp/pub/documents/papers/1996/2DTR/
OpenBoundaries/Figs.tar.g
Causality violation and singularities
We show that singularities necessarily occur when a boundary of causality
violating set exists in a space-time under the physically suitable assumptions
except the global causality condition in the Hawking-Penrose singularity
theorems. Instead of the global causality condition, we impose some
restrictions on the causality violating sets to show the occurrence of
singularities.Comment: 11 pages, latex, 2 eps figure
String Theoretical Interpretation for Finite N Yang-Mills Theory in Two-Dimensions
We discuss the equivalence between a string theory and the two-dimensional
Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which
can be interpreted as a sum of covering maps from closed string world-sheets to
the target space, whose covering number is less than N. This gives an
asymptotic expansion of 1/N whose large N limit becomes the chiral sector
defined by D.Gross and W.Taylor. We also discuss that the residual part of the
partition function provides the non-perturbative corrections to the
perturbative expansion.Comment: 15 pages, no figures, LaTeX2e, typos corrected, final version to
appear in Modern Physics Letters
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