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

R. A. Konoplya·C. Molina·A. Zhidenko
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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 $Ψ_{0} \sim t^{-(\ell + 3/2)} \sin{m t}$, $Ψ_{1} \sim t^{-(\ell + 5/2)} \sin{m t}$, $Ψ_{2} \sim t^{-(\ell + 1/2)} \sin{m t}$, while at asymptotically late times the decay law $Ψ\sim t^{-5/6} \sin{(m t)}$ 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 $\sim t^{-5/6} \sin{(m t)}$ \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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R. A. Konoplya, C. Molina, A. Zhidenko. 2007-02-06. Late time tails of the massive vector field in a black hole background. https://doi.org/10.1103/physrevd.75.084004

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