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

@article{Bizon2007LatetimeTO, title={Late-time tails of a Yang–Mills field on Minkowski and Schwarzschild backgrounds}, author={Piotr Bizo'n and Tadeusz Chmaj and Andrzej Rostworowski}, journal={Classical and Quantum Gravity}, year={2007}, volume={24}, pages={F55 - F63} }

We study the late-time behaviour 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 possess 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 numerically confirm its accuracy.

## 11 Citations

### A Yang–Mills field on the extremal Reissner–Nordström black hole

- Mathematics
- 2016

We consider a spherically symmetric (magnetic) SU(2) Yang–Mills field propagating on the exterior of the extremal Reissner–Nordström black hole. Taking advantage of the conformal symmetry, we reduce…

### Hyperboloidal Einstein-matter evolution and tails for scalar and Yang–Mills fields

- Physics, Mathematics
- 2013

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### Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space

- Mathematics
- 2014

We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius…

### Asymptotics of Schwarzschild black hole perturbations

- Physics
- 2009

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge–Wheeler–Zerilli equations in a time domain using hyperboloidal surfaces and a compactifying radial…

### Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

- Physics
- 2008

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen–Press equation. Compactification along hyperboloidal surfaces in a…

### A scattering theory construction of dynamical vacuum black holes

- Physics, Mathematics
- 2013

We construct a large class of dynamical vacuum black hole spacetimes whose exterior geometry asymptotically settles down to a fixed Schwarzschild or Kerr metric. The construction proceeds by solving…

### Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

- Physics
- 2018

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work,…

### A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

- Mathematics, Physics
- 2011

### Testing the black hole ‘no-hair’ hypothesis

- Physics
- 2016

Black holes (BHs) in general relativity (GR) are very simple objects. This property, that goes under the name of ‘no-hair’, has been refined in the last few decades and admits several versions. The…

### Tails for the Einstein–Yang–Mills system

- Physics, Mathematics
- 2009

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.…

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