Many theorems have been derived that characterize the generic properties of four-dimensional stationary black holes that admit an asymptotically-timelike Killing vector. First, they have one additional axial Killing vector – they are axisymmetric3 – and their event horizon is a Killing horizon4. In asymptotically-flat spacetimes, black holes have spherical topology .
Extremal black holes are defined as stationary black holes with vanishing Hawking temperature,
No physical process is known that would make an extremal black hole out of a non-extremal black hole.5 If one attempts to send finely-tuned particles or waves into a near-extremal black hole in order to further approach extremality, one realizes that there is a smaller and smaller window of parameters that allows one to do so when approaching extremality. In effect, a near-extremal black hole has a potential barrier close to the horizon, which prevents it from reaching extremality. Also, if one artificially continues the parameters of the black holes beyond the extremality bound in a given solution, one typically obtains a naked singularity instead of a black hole. Such naked singularities are thought not to be reachable, which is known as the cosmic censorship hypothesis. Extremal black holes can then be thought of as asymptotic or limiting black holes of physical black holes. The other way around, if one starts with an extremal black hole, one can simply throw in a massive particle to make the black hole non-extremal. Therefore, extremal black holes are finely tuned black holes. Nevertheless, as we will discuss, studying the extremal limit is very interesting because many simplifications occur and powerful specialized methods can be used.
Extremal spinning or charged rotating black holes enjoy several interesting properties that we will summarize below. In order to be self-contained, we will also first provide some properties of generic (extremal or non-extremal) black holes. We refer the reader to the excellent lecture notes  for the derivation of most of these properties.
The combined effect of rotation and charge allows one to extract energy in the range13), the absorption probability is negative because the outgoing flux of energy is higher than the incoming flux.
Living Rev. Relativity 15, (2012), 11
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