Submitted on 9 Jun 2008 (v1), last revised 9 Jun 2008 (this version, v2).-- Latex2e, 53 pages, 2 figures.
We find the general form of all the supersymmetric configurations and solutions of N=2,d=4 Einstein-Yang-Mills theories. In the timelike case, which we study in great detail, giving many examples, the solutions to the full supergravity equations can be constructed from known flat spacetime solutions of the Bogomol'nyi equations. This allows the regular supersymmetric embedding in supergravity of regular monopole solutions ('t Hooft-Poyakov's, Weinberg's, Wilkinson and Bais's) but also embeddings of irregular solutions to the Bogomol'nyi equations which turn out to be regular black holes with different forms of non-Abelian hair once the non-triviality of the spacetime metric is taken into account. The attractor mechanism is realized in a gauge-covariant way. In the null case we determine the general equations that supersymmetric configurations and solutions must satisfy but we do not find relevant new supersymmetric solutions.
This work has been supported in part by the Spanish Ministry of Science and Education
grants FPU AP2004-2574 (MH), FPA2006-00783 and PR2007-0073 (TO), the Comunidad de Madrid grant HEPHACOS P-ESP-00346, by the EU Research Training Network Constituents,
Fundamental Forces and Symmetries of the Universe MRTN-CT-2004-005104, the Spanish Consolider-Ingenio 2010 program CPAN CSD2007-00042 and by the European Social Fund through an I3P-doctores scholarship (PM).