Late time tails of the massive vector field in a black hole background

Abstract

We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild-de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is represented by three functions with different decay law ${\Psi }_0\sim t^{-(\ell +3/2)}\sin mt$, ${\Psi }_1\sim t^{-(\ell +5/2)}\sin mt$, ${\Psi }_2\sim t^{-(\ell +1/2)}\sin mt$, while at asymptotically late times the decay law $\Psi \sim t^{-5/6}\sin (mt)$ is universal, and does not depend on the multipole number $\ell$. Together with previous study of massive scalar and Dirac fields where the same asymptotically late-time decay law was found, it means, that the asymptotically late-time decay law $\sim t^{-5/6}\sin (mt)$ \emph{does not depend} also \emph{on the spin} of the field under consideration. For Schwarzschild-de Sitter black holes it is observed two different regimes in the late-time decay of perturbations: non-oscillatory exponential damping for small values of $m$ and oscillatory quasinormal mode decay for high enough $m$. Numerical and analytical results are found for these quasinormal frequencies.

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• Quasi-Normal Modes of Brane-Localised Standard Model Fields
• Unitary evolution of perturbations of a two-dimensional black hole

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