Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes

An l-pole perturbation in Schwarzschild spacetime generally falls off at late times t as t-2l-3. It has recently been pointed out by Karkowski, Swierczynski, 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-2l-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