THOMAS PRECESSION IN POST-NEWTONIAN GRAVITOELECTROMAGNETISM

The well-known Thomas precession effect is discussed in the context of the post-Newtonian approximation to general relativity using the lang uage of gravitoelectromagnetism (3-plus-1 splitting of gravitational t heory). Preliminary discussion anchors the post-Newtonian coordinate s ystem and choice of gravitational variables in the mathematical struct ure of fully nonlinear general relativity, linking the post-Newtonian gravitoelectric and gravitomagnetic fields to kinematical properties o f the associated observer congruence. The transformation laws for thes e fields under a change of post-Newtonian coordinate system are derive d first within the post-Newtonian theory and then by taking the limit of their fully nonlinear form to reveal the interpretation of the vari ous terms in the post-Newtonian case. These transformation laws are th en used to make a case for the existence of a gravitational analogue o f the ordinary Thomas precession of the spin of a gyroscope.