1 | This is no longer true if the field equations involve not only the Ricci tensor but also the Weyl tensor, such as in Lovelock theories. | |

2 | It follows that the introduction of a length scale, for instance in the form of a (negative) cosmological constant, is a necessary condition for the existence of a black hole in dimensions. But gravity may still remain topological. | |

3 | It has been shown that this requires an infinite affine parameter distance along the null-geodesics generators of the horizon [142]. However, it may still take finite time as measured by an external observer [190]. | |

4 | This choice corresponds to rotation in the positive sense (i.e., increasing ). The solution presented in [200] is obtained by , which gives rotation in a negative sense. | |

5 | An alternative form was found in [140]. The relation between the two is given in [84]. | |

6 | An equivalent system, but with a cosmological interpretation under a Wick rotation of the coordinates , is discussed in [86], along with some simple solution-generating techniques. | |

7 | The classical effective field theory of [49, 168] is an alternative to matched asymptotic expansions, which presumably should be useful as well in the context discussed in this section. | |

8 | The is not round for known solutions, but one can define an effective scale as the radius of a round with the same area. | |

9 | Supersymmetric solutions admit a globally defined Killing vector field that is timelike or null. The assumption is that it is non-null everywhere outside the horizon. | |

10 | The same assumption as for the , case just discussed. | |

11 | The “topological black holes” with , and toroidal or hyperbolic horizons [15] are excluded from our review by their asymptotics. | |

12 | Note that topological censorship can be used to exclude the existence of topologically nonspherical black holes in [97]. | |

13 | Note that this does not disagree with the stability result of [164] for Reissner–Nordström-AdS since the instability involves scalar fields and hence cannot be seen within minimal gauged supergravity. |

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