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

## TL;DR

This paper analyzes the late-time decay of spherically symmetric Yang-Mills fields on Minkowski and Schwarzschild backgrounds, showing solutions decay as t^{-4} and deriving a formula for the tail amplitude.

## Contribution

It provides the first detailed analysis of late-time tails for Yang-Mills fields on these backgrounds, including a third-order formula for the tail amplitude on Minkowski space.

## Key findings

- Solutions decay as t^{-4} at timelike infinity.
- Derived a third-order formula for tail amplitude on Minkowski background.
- Numerical confirmation of the tail amplitude formula.

## 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.