Figure 21: The region , defined by
Equation (128), in the Kerr spacetime. The picture is
purely spatial and shows a meridional
section , with
the axis of symmetry at the left-hand boundary. Through each point of there is a spherical geodesic.
Along each of these spherical geodesics, the coordinate oscillates between extremal
values, corresponding to boundary points of . The
region meets the axis at
radius , given by
.
Its boundary intersects the equatorial
plane in circles of radius (corotating circular light ray) and (counter-rotating circular
light ray). are
determined by and . In
the Schwarzschild limit the region shrinks to the light sphere . In the extreme Kerr limit the region extends to the horizon
because in this limit both and ; for a caveat, as to geometric
misinterpretations of this limit (see
Figure 3 in [16]).
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