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 Psi(0)similar to t(-(l+3/2))sinmt, Psi(1)similar to t(-(l+5/2))sinmt, Psi(2)similar to t(-(l+1/2))sinmt, while at asymptotically late times the decay law Psi similar to t(-5/6)sin(mt) is universal and does not depend on the multipole number l. 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 similar to t(-5/6)sin(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.