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

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

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