Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds

We study the late-time behavior of spherically symmetric solutions of the Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using nonlinear perturbation theory we show in both cases that solutions having smooth compactly supported initial data posses tails which decay as $t^{-4}$ at timelike infinity. Moreover, for small initial data on Minkowski background we derive the third-order formula for the amplitude of the tail and confirm numerically its accuracy.Comment: 7 pages, 3 figure

On weakly turbulent instability of anti-de Sitter space (Preprint)

We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies

On vacuum gravitational collapse in nine dimensions

We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.Comment: 4 pages, 4 figure

Vacuum gravitational collapse in nine dimensions

We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black-hole formation

Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime

We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills field propagating outside the Schwarzschild black hole. Although solutions starting from smooth finite energy initial data remain smooth for all times, not all of them scatter since there are non-generic solutions which asymptotically tend to unstable static solutions. We show that a static solution with one unstable mode appears as an intermediate attractor in the evolution of initial data near a border between basins of attraction of two different vacuum states. We study the saddle-point dynamics near this attractor, in particular we identify the universal phases of evolution: the ringdown approach, the exponential departure, and the eventual decay to one of the vacuum states.Comment: 15 pages, 5 figure

Tails for the Einstein-Yang-Mills system

We study numerically the late-time behaviour of the coupled Einstein Yang-Mills system. We restrict ourselves to spherical symmetry and employ Bondi-like coordinates with radial compactification. Numerical results exhibit tails with exponents close to -4 at timelike infinity $i^+$ and -2 at future null infinity \Scri.Comment: 12 pages, 5 figure

Late-time tails of a self-gravitating massless scalar field, revisited

We discuss the nonlinear origin of the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in even-dimensional spacetimes. Using third-order perturbation method, we derive explicit expressions for the tail (the decay rate and the amplitude) for solutions starting from small initial data and we verify this prediction via numerical integration of the Einstein-scalar field equations in four and six dimensions. Our results show that the coincidence of decay rates of linear and nonlinear tails in four dimensions (which has misguided some tail hunters in the past) is in a sense accidental and does not hold in higher dimensions.Comment: 10 pages, 6 figures, one reference added, updated to conform with published versio

Pion light cone wave function in the non-local NJL model

We use the simple instanton motivated NJL-type model to calculate the leading twist pion light cone wave function. The model consists in employing the momentum dependent quark mass in the quark loop entering the definition of the wave function. The result is analytical up to a solution of a certain algebraic equation. Various properties including the kT dependence of the pion wave function are discussed. The resulting kT integrated wave function is not asymptotic and is in agreement with recent analysis of the CLEO data.Comment: 9 pages, 12 figures, formulas (23-25) corrected, typos correcte