On the method of virtual quanta and gravitational radiation

Abstract

We extend the Weizsäeker-Williams method of virtual quanta to the domain of gravitational encounters and set up a correlation between collision problems and the corresponding interaction of gravitational radiation. In the local rest frame of a relativistic test particle the gravitational field of a Schwarzschild mass consists predominantly of a pulse of plane-fronted gravitational waves. We Fourier analyse this equivalent pulse and consider the scattering of each frequency component, virtual quanta, by the test body. The scattering by the long-range Newtonian-type field of a point particle is described by the analogue of the Rutherford cross-section. The escape of this scattered flux to infinity, suitably transformed, gives us the radiative loss of gravitational energy by a rapidly moving particle. The radiation spectrum and total energy radiated in a distant brehmsstrahlung encounter are computed as an example.