SCATTERING OF MASSLESS SCALAR WAVES BY A SCHWARZSCHILD BLACK-HOLE - APHASE-INTEGRAL STUDY

Plane scalar waves scattered off a Schwarzschild black hole are studie d in the partial-wave picture. A new approximate formula for the relev ant phase shifts is derived using the phase-integral method. This form ula is, in principle, uniformly valid for all frequencies and agrees w ith well-known approximations for frequencies well above and below the top of the curvature potential barrier. The reliability of the phase- integral formula is assessed in two different ways. First we use the f act that higher orders of approximation are easily implemented in the phase-integral method. The accuracy of each phase shift can be estimat ed by the contribution to it by the following order of approximation. Second, we use the approximate phase shifts to construct physically me aningful quantities, such as the deflection function and cross section , for several scattering frequencies. The features of these quantities , especially those associated with the prominent black-hole glory in t he backward direction, are in excellent agreement with results of prev ious studies of the problem. The new phase-shift formula is thus shown to be reliable and provides a useful and efficient tool, especially f or intermediate and high frequencies.