88 research outputs found
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 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 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
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