Gravitational waves

Abstract

The theory of weak gravitational waves is discussed at length. The transverse traceless gauge is described, and the behaviour of plane wave solutions obtained. The impact of a wave on physical objects, and hence methods for their detection, are calculated. The laser interferometric gravitational wave detector is described. Sources such as binary stars are considered. The compact source approximation is employed, and the quadrupole formula relating the wave amplitude to the quadrupole of the source is obtained. Energy flux in gravitational waves is calculated by two methods, one more general, the other giving further physical insight. The total emitted power is obtained. These are lengthy calculations but they are presented in full. Finally they are applied in detail to a binary star with elliptical orbtis (the Hulse Taylor binary) and to a black hole merger detected by the LIGO interferometers.