Geodesic deviation at null infinity and the physical effects of very long wave gravitational radiation

Abstract

Given the news function$\dot \sigma$ of a radiating space-time describing an isolated source, one can construct two physically important functions on the infinite celestial sphere surrounding the source:

$$\int_{ - \infty }^\infty {\dot \sigma \dot \bar \sigma d\tau } and \int_{ - \infty }^\infty {\dot \sigma d\tau (\tau = {\rm B}ondi parameter)} $$

The first describes the energy flux of radiation through the sphere and is the dominant function for high-frequency radiation. The second function contains information about the very low-frequency radiation and dominates at such frequencies. The physical effects of this function are investigated, and it is shown that, even for an arbitrarily small energy flux, it can cause a finite amount of geodesic deviation in the radiation zone. An explicit formula for this deviation is obtained in the case of a bifurcating star in the low-frequency approximation where the energy flux can be neglected.