GENERAL-SOLUTION AND CLASSIFICATION OF CONFORMAL MOTIONS IN STATIC SPHERICAL SPACETIMES

We find the complete and explicit general solution of the conformal Ki lling equation in static spherically symmetric spacetimes, thus unifyi ng and generalizing previous special cases. For non-conformally-kat sp acetimes, there are at most two proper conformal motions. There are th ree classes of such spacetimes, and one or both of the conformal Killi ng vectors is non-inheriting. One of the classes includes self-similar spacetimes (i.e. with a homothetic motion). The conformally flat spac etimes (including the Schwarzschild interior metric) fall into three c lasses, and their eleven proper conformal Killing vectors are given in full. The only spacetimes with conformal motion that are regular at t he centre are conformally flat.