6,038 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
Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology
Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in
circulating the file, due to technical problems now fixe
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
Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity
A theory recently proposed by the author aims to explain decoherence and the
thermodynamical behaviour of closed systems within a conservative, unitary,
framework for quantum gravity by assuming that the operators tied to the
gravitational degrees of freedom are unobservable and equating physical entropy
with matter-gravity entanglement entropy. Here we obtain preliminary results on
the extent of decoherence this theory predicts. We treat first a static state
which, if one were to ignore quantum gravitational effects, would be a quantum
superposition of two spatially displaced states of a single classically well
describable ball of uniform mass density in empty space. Estimating the quantum
gravitational effects on this system within a simple Newtonian approximation,
we obtain formulae which predict e.g. that as long as the mass of the ball is
considerably larger than the Planck mass, such a would-be-coherent static
superposition will actually be decohered whenever the separation of the centres
of mass of the two ball-states excedes a small fraction (which decreases as the
mass of the ball increases) of the ball radius. We then obtain a formula for
the quantum gravitational correction to the would-be-pure density matrix of a
non-relativistic many-body Schroedinger wave function and argue that this
formula predicts decoherence between configurations which differ (at least) in
the "relocation" of a cluster of particles of Planck mass. We estimate the
entropy of some simple model closed systems, finding a tendency for it to
increase with "matter-clumping" suggestive of a link with existing
phenomenological discussions of cosmological entropy increase.Comment: 11 pages, plain TeX, no figures. Accepted for publication as a
"Letter to the Editor" in "Classical and Quantum Gravity
The effect of Pressure in Higher Dimensional Quasi-Spherical Gravitational Collapse
We study gravitational collapse in higher dimensional quasi-spherical
Szekeres space-time for matter with anisotropic pressure. Both local and global
visibility of central curvature singularity has been studied and it is found
that with proper choice of initial data it is possible to show the validity of
CCC for six and higher dimensions. Also the role of pressure in the collapsing
process has been discussed.Comment: 11 pages, 6 figures, RevTeX styl
Non-spherical collapse of a two fluid star
We obtain the analogue of collapsing Vaidya-like solution to include both a
null fluid and a string fluid, with a linear equation of state (), in non-spherical (plane symmetric and cylindrically symmetric) anti-de
Sitter space-timess. It turns out that the non-spherical collapse of two fluid
in anti-de Sitter space-times, in accordance with cosmic censorship, proceed to
form black holes, i.e., on naked singularity ever forms, violating hoop
conjecture.Comment: 7 pages, RevTeX 4, minor correction
Thermal gravity, black holes and cosmological entropy
Taking seriously the interpretation of black hole entropy as the logarithm of
the number of microstates, we argue that thermal gravitons may undergo a phase
transition to a kind of black hole condensate. The phase transition proceeds
via nucleation of black holes at a rate governed by a saddlepoint configuration
whose free energy is of order the inverse temperature in Planck units. Whether
the universe remains in a low entropy state as opposed to the high entropy
black hole condensate depends sensitively on its thermal history. Our results
may clarify an old observation of Penrose regarding the very low entropy state
of the universe.Comment: 5 pages, 2 figures, RevTex. v4: to appear in Phys. Rev.
Can we see naked singularities?
We study singularities which can form in a spherically symmetric
gravitational collapse of a general matter field obeying weak energy condition.
We show that no energy can reach an outside observer from a null naked
singularity. That means they will not be a serious threat to the Cosmic
Censorship Conjecture (CCC). For the timelike naked singularities, where only
the central shell gets singular, the redshift is always finite and they can in
principle, carry energy to a faraway observer. Hence for proving or disproving
CCC the study of timelike naked singularities will be more important. Our
results are very general and are independent of initial data and the form of
the matter.Comment: 10 page
Outgoing gravitational shock-wave at the inner horizon: The late-time limit of black hole interiors
We investigate the interiors of 3+1 dimensional asymptotically flat charged
and rotating black holes as described by observers who fall into the black
holes at late times, long after any perturbations of the exterior region have
decayed. In the strict limit of late infall times, the initial experiences of
such observers are precisely described by the region of the limiting stationary
geometry to the past of its inner horizon. However, we argue that late
infall-time observers encounter a null shockwave at the location of the
would-be outgoing inner horizon. In particular, for spherically symmetric black
hole spacetimes we demonstrate that freely-falling observers experience a
metric discontinuity across this shock, that is, a gravitational shock-wave.
Furthermore, the magnitude of this shock is at least of order unity. A similar
phenomenon of metric discontinuity appears to take place at the inner horizon
of a generically-perturbed spinning black hole. We compare the properties of
this null shockwave singularity with those of the null weak singularity that
forms at the Cauchy horizon.Comment: 23 pages, 4 figures, minor change
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