Late-time evolution of the Yang-Mills field in the spherically symmetric gravitational collapse

TL;DR

This paper studies how Yang-Mills fields decay over time in different black hole spacetimes, revealing distinct late-time behaviors influenced by spacetime curvature and field self-interactions.

Contribution

It provides a detailed comparison of late-time Yang-Mills field evolution in Schwarzschild and Reissner-Nordström backgrounds, highlighting the effects of curvature and self-interaction.

Findings

Late-time tails in Schwarzschild resemble scalar field tails with l=1.

Reissner-Nordström tails are smaller and oscillatory.

Decay dominated by spacetime curvature in Schwarzschild, self-interaction in Reissner-Nordström.

Abstract

We investigate the late-time evolution of the Yang-Mills field in the self-gravitating backgrounds: Schwarzschild and Reissner-Nordstr\"om spacetimes. The late-time power-law tails develop in the three asymptotic regions: the future timelike infinity, the future null infinity and the black hole horizon. In these two backgrounds, however, the late-time evolution has quantitative and qualitative differences. In the Schwarzschild black hole background, the late-time tails of the Yang-Mills field are the same as those of the neutral massless scalar field with multipole moment l=1. The late-time evolution is dominated by the spacetime curvature. When the background is the Reissner-Nordstr\"om black hole, the late-time tails have not only a smaller power-law exponent, but also an oscillatory factor. The late-time evolution is dominated by the self-interacting term of the Yang-Mills field. The cause responsible for the differences is revealed.