We discussed that near-horizon geometries of compact extremal black holes are isolated systems with universal properties and we reviewed that in all analyzed cases they have no local bulk dynamics. Given the non-trivial thermodynamic properties of these systems even at extremality, one can suspect that some non-trivial dynamics are left. It turns out that such non-trivial dynamics appears at the boundary of the near-horizon geometry. We now show that near-horizon geometries can be extended to a large class describing extremal boundary excitations. The set of all near-horizon geometries will admit additional symmetries at their boundary – asymptotic symmetries – which will turn out to be given by one copy of the Virasoro algebra. We will then argue that these near-horizon geometries are described by chiral limits of two-dimensional CFTs, which we will use to microscopically derive the entropy of any charged or spinning extremal black hole.
http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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