An $\ell$-pole perturbation in Schwarzschild spacetime generally falls off at late times $t$ as $t^{-2\ell -3}$. It has recently been pointed out by Karkowski, Świerczyński, and Malec, that for initial data that is of compact support, and is initially momentarily static, the late-time behavior is different, going as $t^{-2\ell -4}$. By considering the Laplace transforms of the fields, we show here why the momentarily stationary case is exceptional. We also explain, using a time-domain description, the special features of the time development in this exceptional case.

• Received 23 August 2004

DOI:https://doi.org/10.1103/PhysRevD.70.084039