WAVE-PROPAGATION IN GRAVITATIONAL SYSTEMS - LATE-TIME BEHAVIOR

It is well known that the dominant late time behavior of waves propaga ting on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic t reatment of the tail phenomenon for a broad class of models via a Gree n's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function (G) over tilde(ome ga) along the -Im omega axis, generalizing the Schwarzschild result. ( ii) The omega dependence of the cut is determined by the asymptotic bu t not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a st ar as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case w ith a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and t he time dependence of the tail for a broad class of models are obtaine d analytically (v) The analytical results are in perfect with numerica l calculations.