3,209 research outputs found
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
Gaussian limits for multidimensional random sequential packing at saturation (extended version)
Consider the random sequential packing model with infinite input and in any
dimension. When the input consists of non-zero volume convex solids we show
that the total number of solids accepted over cubes of volume is
asymptotically normal as . We provide a rate of
approximation to the normal and show that the finite dimensional distributions
of the packing measures converge to those of a mean zero generalized Gaussian
field. The method of proof involves showing that the collection of accepted
solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case
We have studied spacetime structures of static solutions in the
-dimensional Einstein-Gauss-Bonnet-Maxwell- system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient is non-negative and in
order to define the relevant vacuum state. Solutions have the
-dimensional Euclidean sub-manifold whose curvature is , or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius for any mass parameter. There the Kretschmann invariant
behaves as , which is much milder than divergent behavior of
the central singularity in general relativity . Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with and have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.Comment: 20 pages, 10 figure
Beyond the veil: Inner horizon instability and holography
We show that scalar perturbations of the eternal, rotating BTZ black hole
should lead to an instability of the inner (Cauchy) horizon, preserving strong
cosmic censorship. Because of backscattering from the geometry, plane wave
modes have a divergent stress tensor at the event horizon, but suitable
wavepackets avoid this difficulty, and are dominated at late times by
quasinormal behavior. The wavepackets have cuts in the complexified coordinate
plane that are controlled by requirements of continuity, single-valuedness and
positive energy. Due to a focusing effect, regular wavepackets nevertheless
have a divergent stress-energy at the inner horizon, signaling an instability.
This instability, which is localized behind the event horizon, is detected
holographically as a breakdown in the semiclassical computation of dual CFT
expectation values in which the analytic behavior of wavepackets in the
complexified coordinate plane plays an integral role. In the dual field theory,
this is interpreted as an encoding of physics behind the horizon in the
entanglement between otherwise independent CFTs.Comment: 40 pages, LaTeX, 3 eps figures, v2: references adde
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Quasi-local energy-momentum and energy flux at null infinity
The null infinity limit of the gravitational energy-momentum and energy flux
determined by the covariant Hamiltonian quasi-local expressions is evaluated
using the NP spin coefficients. The reference contribution is considered by
three different embedding approaches. All of them give the expected Bondi
energy and energy flux.Comment: 14 pages, accepted by Phys.Rev.
On the well posedness of Robinson Trautman Maxwell solutions
We show that the so called Robinson-Trautman-Maxwell equations do not
constitute a well posed initial value problem. That is, the dependence of the
solution on the initial data is not continuous in any norm built out from the
initial data and a finite number of its derivatives. Thus, they can not be used
to solve for solutions outside the analytic domain.Comment: 9 page
Asymptotic twistor Theory and the Kerr Theorem
We first review asymptotic twistor theory with its real subspace of null
asymptotic twistors. This is followed by a description of an asymptotic version
of the Kerr theorem that produces regular asymptotically shear free null
geodesic congruences in arbitrary asymptotically flat Einstein or
Einstein-Maxwell spacetimes.Comment: 1
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