The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by $\psi \mathrm{}\left(t\right)\mathrm{}\sim t^{-5/6}\sin \left[\omega \mathrm{}\right(t)\mathrm{}\times t],$ where $\omega \mathrm{}\left(t\right)\mathrm{}$ depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of $-5/6$ depends on neither the multipole mode $\mathcal{l}$ nor on the spin rate of the black hole $a/M.\mathrm{}$ In all black hole spacetimes, massive scalar fields have the same late-time behavior irrespective of their initial data (i.e., angular distribution). Their late-time behavior is universal.

• Received 3 March 2004

DOI:https://doi.org/10.1103/PhysRevD.70.044018