What happens to Petrov classification on horizons of axisymmetric dirty black holes

@article{Tanatarov2014WhatHT,
  title={What happens to Petrov classification on horizons of axisymmetric dirty black holes},
  author={I. V. Tanatarov and O. B. Zaslavskii},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={022502}
}
We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of an observer on a circular orbit. We call this entity the boosted Petrov type (BPT), as the corresponding frame is obtained by a singular boost from the regular one. The PT off… 
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