Superradiance and Instability of Black Holes

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The stability of black holes has a crucial importance when we study their formation and fate in Nature. It also has an intimate relation with the cosmic censorship hypothesis. For these reasons, this problem has been studied for a long time, and uniqueness and perturbative stability were established for most asymptotically flat black holes in the four-dimensional Einstein-Maxwell system except for the KerrNewman black hole. 1),2) When we go beyond this classical system, we encounter various new situations. One such extension is to consider systems containing other types of matter. Very interesting examples are the Einstein-Skyrme system and the Einstein-Yang-Mills system. These systems have three families of static asymptotically flat spherically symmetric solutions; a soliton family, a hairy black hole family and the vacuum one. These all families of solutions were shown to be stable numerically for the EinsteinSkyrme system while for the EYM system, the colored black holes and the soliton solutions were shown to be unstable (see Ref. 3) for review). Hence, in the latter case, the uniqueness theorem holds practically. Another extension motivated by recent progresses in unified theories is to consider higher-dimensional black holes. In the static AF Einstein-Maxwell system, the uniqueness theorem still holds in higher dimensions. Further, in the vacuum case, the Schwarzschild-Tangherlini solution was shown to be stable 4) by using the extension of the Regge-Wheeler and Zerilli equations to higher dimensions, 5) although the stability of the charged static black hole was proved only for D = 5 analytically 6) and for 6 ≤ D ≤ 11 numerically. 7)