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

Abstract

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.

7 pages, 3 figures

Cited by in corpus (17)

• Testing the black hole "no-hair" hypothesis
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
• Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• A scattering theory construction of dynamical vacuum black holes
• Asymptotics of Schwarzschild black hole perturbations
• A hyperboloidal study of tail decay rates for scalar and Yang-Mills fields
• Possible discovery of a nonlinear tail and second-order quasinormal modes in black hole ringdown
• Late-time tails of a self-gravitating massless scalar field, revisited
• Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime
• Linear and nonlinear tails II: exact decay rates in spherical symmetry
• Late-time tails of wave maps coupled to gravity
• Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system
• A Yang-Mills field on the extremal Reissner-Nordström black hole
• Tails for the Einstein-Yang-Mills system
• A note on late-time tails of spherical nonlinear waves