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 $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\alpha$ is non-negative and $4{\tilde \alpha}/\ell^2\leq 1$ in order to define the relevant vacuum state. Solutions have the $(n-2)$-dimensional Euclidean sub-manifold whose curvature is $k=1,~0$, 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 $r=r_b>0$ for any mass parameter. There the Kretschmann invariant behaves as $O((r-r_b)^{-3})$, which is much milder than divergent behavior of the central singularity in general relativity $O(r^{-4(n-2)})$. 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 $k=-1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k=-1$ and $n\geq6$ 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