Gravitational Scattering of a Quantum Particle and the Privileged Coordinate System

In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschildmetrics in standard, harmonic, and other coordinate systems in linear and G²-approximations. In general, different coordinate systems lead to different scattering. This opens up the possibility to choose the privileged coordinate system which should lead to scattering in agreement with experiment.