Non-supersymmetric attractors inR2gravities

We investigate the attractor mechanism for spherically symmetric extremalblack holes in a theory of general $R^2$ gravity in 4-dimensions, coupled togauge fields and moduli fields. For the general $R^2$ theory, we look forsolutions which are analytic near the horizon, show that they exist and enjoythe attractor behavior. The attractor point is determined by extremization ofan effective potential at the horizon. This analysis includes the backreactionand supports the validity of non-supersymmetric attractors in the presence ofhigher derivative interactions. To include a wider class of solutions, wecontinue our analysis for the specific case of a Gauss-Bonnet theory which isnon-topological, due to the coupling of Gauss-Bonnet terms to the modulifields. We find that the regularity of moduli fields at the horizon issufficient for attractor behavior. For the non-analytic sector, this regularitycondition in turns implies the minimality of the effective potential at theattractor point.Comment: 19 pages, 2 figure