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

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 Ψ₀~t^-(+3/2)sinmt, Ψ₁~t^-(+5/2)sinmt, Ψ₂~t^-(+1/2)sinmt, while at asymptotically late times the decay law Ψ~t^-5/6sin(mt) is universal and does not depend on the multipole number . Together with a 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 ~t^-5/6sin(mt) does not depend also on the spin of the field under consideration. For Schwarzschild--de Sitter black holes it is observed in two different regimes in the late-time decay of perturbations: nonoscillatory 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.