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 [200Jump To The Next Citation Point] 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 [84Jump To The Next Citation Point].
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.