List of Footnotes

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 $2+ 1$ 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 $φ$ ). The solution presented in [200 ] is obtained by $φ → − φ$ , 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 $(t,r,z) → (x,t,&tidle;z)$ , 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 $Sd−3$ is not round for known solutions, but one can define an effective scale $R 2$ as the radius of a round $Sd−3$ 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 $d = 4$ , $N = 2$ case just discussed.
11		The “topological black holes” with $-μ-- r2 U(r) = k − rd−3 + ℓ2$ , $k = 0,− 1$ 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 $AdS4$ [97 ].
13		Note that this does not disagree with the stability result of [164 ] for $d = 4$ Reissner–Nordström-AdS since the instability involves scalar fields and hence cannot be seen within minimal $𝒩 = 2$ gauged supergravity.