Waves in Schwarzschild spacetimes: How strong can imprints of the spacetime curvature be

Emitted radiation can be reprocessed in curved spacetimes, due to the breakdown of the Huyghens principle. A maximization procedure for the energy diffusion allows one to obtain wave packets (gravitational and electromagnetic) that are particularly strongly backscattered. Examples are shown with the backscattered part exceeding by one order the remnants of the initial signals. A robust ringing can be observed, with amplitudes exceeding the leftovers of the main radiation pulse. An analysis of the results obtained allows one to set demands on some parameters in the numerical description of a realistic process of the collapse of two black holes.