3,347 research outputs found
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
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
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
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.
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
Generic Cosmic Censorship Violation in anti de Sitter Space
We consider (four dimensional) gravity coupled to a scalar field with
potential V(\phi). The potential satisfies the positive energy theorem for
solutions that asymptotically tend to a negative local minimum. We show that
for a large class of such potentials, there is an open set of smooth initial
data that evolve to naked singularities. Hence cosmic censorship does not hold
for certain reasonable matter theories in asymptotically anti de Sitter
spacetimes. The asymptotically flat case is more subtle. We suspect that
potentials with a local Minkowski minimum may similarly lead to violations of
cosmic censorship in asymptotically flat spacetimes, but we do not have
definite results.Comment: 4 pages, v2: minor change
Effect of charged partons on black hole production at the Large Hadron Collider
The cross section for black hole production in hadron colliders is calculated
using a factorization hypothesis in which the parton-level process is
integrated over the parton density functions of the protons. The mass, spin,
charge, colour, and finite size of the partons are usually ignored. We examine
the effects of parton electric charge on black hole production using the
trapped-surface approach of general relativity. Accounting for electric charge
of the partons could reduce the black hole cross section by one to four orders
of magnitude at the Large Hadron Collider. The cross section results are
sensitive to the Standard Model brane thickness. Lower limits on the amount of
energy trapped behind the event horizon in the collision of charged particles
are also calculated.Comment: corrected typo in figure 1b; added some clarification in 3 places; 21
pages, 9 figures, JHEP3 forma
Accelerated sources in de Sitter spacetime and the insufficiency of retarded fields
The scalar and electromagnetic fields produced by the geodesic and uniformly
accelerated discrete charges in de Sitter spacetime are constructed by
employing the conformal relation between de Sitter and Minkowski space.
A special attention is paid to new effects arising in spacetimes which, like
de Sitter space, have spacelike conformal infinities. Under the presence of
particle and event horizons, purely retarded fields (appropriately defined)
become necessarily singular or even cannot be constructed at the "creation
light cones" -- future light cones of the "points" at which the sources "enter"
the universe. We construct smooth (outside the sources) fields involving both
retarded and advanced effects, and analyze the fields in detail in case of (i)
scalar monopoles, (ii) electromagnetic monopoles, and (iii) electromagnetic
rigid and geodesic dipoles.Comment: 36 pages, 5 figures, LaTex2e; minor misprints corrected, one
reference added and some terminology change
Shape in an Atom of Space: Exploring quantum geometry phenomenology
A phenomenology for the deep spatial geometry of loop quantum gravity is
introduced. In the context of a simple model, an atom of space, it is shown how
purely combinatorial structures can affect observations. The angle operator is
used to develop a model of angular corrections to local, continuum flat-space
3-geometries. The physical effects involve neither breaking of local Lorentz
invariance nor Planck scale suppression, but rather reply on only the
combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example
of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde
On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields
The convergence of polyhomogeneous expansions of zero-rest-mass fields in
asymptotically flat spacetimes is discussed. An existence proof for the
asymptotic characteristic initial value problem for a zero-rest-mass field with
polyhomogeneous initial data is given. It is shown how this non-regular problem
can be properly recast as a set of regular initial value problems for some
auxiliary fields. The standard techniques of symmetric hyperbolic systems can
be applied to these new auxiliary problems, thus yielding a positive answer to
the question of existence in the original problem.Comment: 10 pages, 1 eps figur
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