Some properties and problems of accretion disks about Kerr naked singularities

Disk accretion onto a Kerr naked singularity is investigated by examining the stable circular equatorial orbits of a test particle in a Kerr background. It is assumed that there is a mechanism (e.g., viscous stress) at large radii that disperses energy and transfers angular momentum outward and mass inward, while maintaining the accretion flow in quasi-geodesic circular orbits. The results obtained show that: (1) the radius and energy of the last stable orbit increase as the ratio of the angular-momentum density and mass (a/M) of the naked singularity increases; (2) for a/M less than the square root of (32/27) there is a region where the energy becomes negative, suggesting that more energy than the mass-energy of a test particle can be extracted; (3) pathologies related to the definition of positive and negative energy states exist for a/M between unity and the square root of (32/27); and (4) the entire mass-energy of a test particle can be extracted for a/M equal to the square root of (32/27).