Solitons and the microscopic entropy of hairy black holes in three dimensions
Abstract: One of the strongest evidences of the AdS/CFT correspondence is provided by three-dimensional gravity with a negative cosmological constant, whose asymptotic symmetry group is the conformal one. As a further example, one can consider gravity coupled to self-interacting scalar field having a slow fall-off at infinity. In these cases, the metric describes an asymptotically AdS spacetime in a relaxed sense as compared with the one of Brown and Henneaux. Nevertheless, the asymptotic symmetry group remains to be the same as in pure gravity. In this talk we show a wide class of scalar hairy black holes, including spinning ones, which fit in these asymptotic conditions. Moreover, for each self-interaction potential there is a soliton, which is a regular solution, devoid of integration constants and with a finite mass, so that they can be naturally regarded as the ground state of the theories for which the scalar fields are switched on. We explain how this assumption allows to reproduce the semiclassical hairy black hole entropy from the asymptotic growth of the number of states by means of Cardy formula.
1:30pm-2:30pm calendar page