I. V. Tanatarov, O. B. Zaslavskii
We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type in the frame of the observer crossing the horizon is different from that in the usual (but singular in the horizon limit) frame of an observer on a circular orbit, and is more general. The effect takes place for all regular metrics, irrespective of the extremality of the horizon. The space-times of Petrov types D and O off-horizon are the only ones, for which the on-horizon type in both frames can be the same and coincide with the algebraic type in its vicinity. The on-horizon mutual alignment of the principal null directions and the generator is studied in detail. As an example, we also analyze a special class of metrics with utra-extremal horizons (for which the regularity conditions look different from the general case) and compare their off-horizon and on-horizon algebraic structure in both frames.
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http://arxiv.org/abs/1211.4376
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