Descripción: It is shown that Born-Infeld gravity -a high energy deformation of Einstein gravity-removes the singularities of a cosmic string. The respective vacuum solution results to be free of conical singularity and closed timelike curves. The space ends at a minimal circle where the curvature invariants vanish; but this circle cannot be reached in a finite proper time. © Published under licence by IOP Publishing Ltd.

Descripción: A logarithmic 1-form on ℂℙn can be written as ω = (Π0m Fj) ∑0m λi dFi/Fi = λ0F̂ 0dF0 +⋯+ λmF̂ mdFm with F̂i = (Π0 m Fj)/Fi for some homogeneous polynomials Fi of degree di and constants λi ∈ ℂ* such that ∑ λidi = 0. For general Fi, λi, the singularities of ω consist of a schematic union of the codimension 2 subvarieties Fi = Fj = 0 together with, possibly, finitely many isolated points. This is the case when all Fi are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities. © Foundation Compositio Mathematica 2006.

Descripción: We obtain a black hole solution in the Einstein-Gauss-Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature TH, the specific heat C, the entropy S, and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking-Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss-Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background. © 2010 Elsevier B.V. All rights reserved.

Descripción: We study a k-essence field evolving linearly with the cosmic time and the atypical k-essence model on a homogeneous and isotropic flat 3-brane. We show that the k-field is driven by an inverse quadratic polynomial potential. The solutions represent expanding, contracting or bouncing universes with a finite time span and some of them end in a big crunch or a big rip. Besides, by selecting the extended tachyonic kinetic functions we analyze the high and low energy limits of our model, obtaining the nearly power law solution. We introduce a tachyon field with negative energy density and show that the universe evolves between two singularities. © 2010 IOP Publishing Ltd.

Descripción: In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime. © 2010 Elsevier B.V.

Descripción: We discuss the production of two hadrons in e+e- annihilation within the framework of perturbative QCD. The cross section for this process is calculated to next-to-leading order accuracy with a selection of variables that allows the consideration of events where the two hadrons are detected in the same jet. In this configuration we contemplate the possibility that the hadrons come from a double fragmentation of a single parton. The double-fragmentation functions required to describe the transition of a parton to two hadrons, are also necessary to completely factorize all collinear singularities. We explicitly show that factorization applies to order αs in the case of two-hadron production. © 2003 Elsevier B.V. All rights reserved.

Descripción: We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 61443 points and three different configurations on grids of 40963 points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity. © 2013 American Physical Society.