Null geodesics in the extended Kerr manifold

The behavior of null geodesics is analyzed for extended Kerr manifolds whose rotation and mass parameters satisfy the condition $0\le {\mathfrak{a}}^2\le m^2$. Geodesics are characterized by their impact parameters; radial and angular barriers, which restrict the motion, are derived in terms of these parameters. The radial barriers are used in determining the ultimate destination of null rays in the extended manifold. In agreement with previous work, there is a "throat," outside the event horizons, through which rays are admitted to the hole; we find in addition an "inner throat," which admits rays to negative radii. The boundary of each throat is determined for various initial ray angles ${\theta }_0$ for holes of particular rotation parameters. The cross-sectional area of the outer throat is rather insensitive to ray and hole parameters, but the inner throat is larger for rays with smaller ${\theta }_0$ or for holes with larger rotation. The throat areas are related to the angular distributions of rays emerging from a hole into various regions of the manifold, after having initially converged upon the hole in a spherically symmetric manner.