Regular Article - Theoretical Physics
Extremal limits and Kerr spacetime
Department of Physics, Vivekananda Satabarshiki Mahavidyalaya, Manikpara, Paschim Medinipur, West Bengal, 721513, India
2 Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, 711 202, India
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Published online: 15 June 2013
The fact that one must evaluate the near-extremal and near-horizon limits of Kerr spacetime in a specific order, is shown to lead to discontinuity in the extremal limit, such that this limiting spacetime differs nontrivially from the precisely extremal spacetime. This is established by first showing a discontinuity in the extremal limit of the maximal analytic extension of the Kerr geometry, given by Carter. Next, we examine the ISCO of the exactly extremal Kerr geometry and show that on the event horizon of the extremal Kerr black hole, it coincides with the principal null geodesic generator of the horizon, having vanishing energy and angular momentum. We find that there is no such ISCO in the near-extremal geometry, thus garnering additional support for our primary contention. We relate this disparity between the two geometries to the lack of a trapping horizon in the extremal situation.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013