Figure 21

Figure 21: The region K, defined by Equation (128View Equation), in the Kerr spacetime. The picture is purely spatial and shows a meridional section f = constant, with the axis of symmetry at the left-hand boundary. Through each point of K there is a spherical geodesic. Along each of these spherical geodesics, the coordinate h oscillates between extremal values, corresponding to boundary points of K. The region K meets the axis at radius rc, given by r3c- 3mr2c + a2rc + ma2 = 0. Its boundary intersects the equatorial plane in circles of radius rph + (corotating circular light ray) and ph r- (counter-rotating circular light ray). ph r± are determined by ph ph 2 2 r± (r± - 3m) = 4ma and r+ < rp+h< 3m < rp-h < 4m. In the Schwarzschild limit a --> 0 the region K shrinks to the light sphere r = 3m. In the extreme Kerr limit a-- > m the region K extends to the horizon because in this limit both rph --> m + and r --> m +; for a caveat, as to geometric misinterpretations of this limit (see Figure 3 in [16]).