The equivalence of precession phenomena in metric theories of gravity

Abstract

The requirement of general covariance imparts to metric theories of gravity, such as general relativity, important structural features. A precise mathematical form results, ensuring that computation of observable physical effects in the theory gives the same answers independently of the chosen system of coordinates. This coordinate independence property, in turn, can lead to an equivalence of apparently different physical effects. An important example is provided by the phenomenon of geodetic precession of a gyroscope as it falls freely in the gravitational field of massive body. A simple argument is presented that demonstrates clearly, without the need for detailed calculation, how geodetic precession of a gyroscope and the effect of frame-dragging are fundamentally equivalent. The argument applies to a general class of metric theories of gravity. There exist potentially important implications of this equivalence for interpreting experiments proposed to test frame-dragging