Parthapratim Pradhan, Parthasarathi Majumdar
In this paper, we investigate a number of issues regarding the disparity between precisely extremely and nearly extremely geometries, the \emph{first} of which concerns the singular nature of the extremal limit of Carter's maximal analytic extension of a generic Kerr geometry and the second one is that the direct Innermost Stable Circular Orbits(ISCO) in extremal Kerr spacetime which lie precisely {\it on} the event horizon in terms of the radial coordinate which coincides with the \emph{principal null geodesic generator}. This type of geodesics are unstable in the corresponding near-extremal situation. We also trying to find the difference between the extremal limit of a generic Kerr spacetime and the exactly extremal geometry. We further prove that the extremal Kerr black hole spacetime don't have any outer trapped surface.
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http://arxiv.org/abs/1108.2333
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