Near-horizon analysis of D=5 BPS black holes and rings

A comprehensive analysis is presented based exclusively on near-horizon data to determine the attractor equations and the entropy of BPS black holes and rings in five space-time dimensions, for a Lagrangian invariant under eight supersymmetries with higher-derivative couplings. For spinning black holes the results only partially agree with the results of previous work, where often additional input was used beyond the near-horizon behaviour. A number of discrepancies remains, for example, pertaining to small black holes and to large spinning black holes, which are related to the presence of the higher-derivative couplings. Arguments are presented to explain some of them. For the black rings, the analysis is intricate due to the presence of Chern-Simons terms and due to the fact that the gauge fields are not globally defined. The contributions from the higher-derivative couplings take a systematic form in line with expectations based on a variety of arguments.