RAPIDLY ROTATING POLYTROPES IN GENERAL-RELATIVITY

We construct an extensive set of equilibrium sequences of rotating pol ytropes in general relativity. We determine a number of important phys ical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial pertur bations is diagnosed. Two classes of evolutionary sequences of fixed r est mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leadi ng to loss of angular momentum causes a star to evolve in a quasi-stat ionary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Prior t o collapse, the star must spin up as it loses angular momentum, an eff ect which may provide an observational precursor to gravitational coll apse to a black hole.