Extremal Limits and Kerr Spacetime

Details Extremal Limits and Kerr Spacetime Extremal Limits and Kerr Spacetime

2011-08-11

arxiv.org/abs/1108.2333v4

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 Pages, Latex 2e, no figures

Scientific paper

We study Innermost Stable Circular Orbits (ISCO) in extremal Kerr spacetime which lie close (in terms of the radial coordinate) to the event horizon and compare these with similar orbits in the near-extremal situation. Extremization of the effective potential for timelike circular orbits shows the existence of a stable circular geodesics in the extremal spacetime, precisely {\it on} the event horizon in terms of the radial coordinate. This type of geodesics is unstable in the corresponding near-extremal spacetime as we show here, testifying to differences between the extremal limit of a generic Kerr spacetime and the exactly extremal geometry. Another aspect of the extremization of the effective potential for null circular orbits shows the existence of an unstable circular geodesic due to the axisymmetry of the spacetime in the extremal Kerr black hole. We attempt to relate this to the fact that the extremal Kerr black hole spacetime possesses no outer trapped surface.

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