Gravitational collapse of rotating spheroids and the formation of naked singularities

We explore numerically the effect of rotation on the collapse of collisionless gas spheroids in full general relativity. The spheroids are initially prolate and consist of equal numbers of corotating and counterrotating particles. We have previously shown that in the absence of rotation the spheroids all collapse to spindle singularities. When the spheroids are sufficiently compact, the singularities are hidden inside black holes. However, when the spheroids are large enough, there are no apparent horizons. These nonrotating spheroids are strong candidates for naked singularities. Here our simulations suggest that rotation significantly modifies the evolution when it is sufficiently large. Imploding configurations with appreciable rotation ultimately collapse to black holes. However, for small enough angular momentum, our simulations cannot at present distinguish rotating from nonrotating collapse: spindle singularities appear to arise without apparent horizons. Hence it is possible that even spheroids with some angular momentum may form naked singularities.