SYMMETRIES AND BLACK HOLESIN N = 2GAUGED SUPERGRAVITY

The main goal of this work is to explore the role and the power of the Hamilton-Jacobi approach and solutions generating techniques to search black hole solutions in abelian gauged supergravity theories. After a brief introduction explaining how supergravity arises as effective theory of superstrings, a chapter is devoted to the detailed description of N = 2 abelian gauged supergravity in d = 4 and d = 5. The study of the equations of motion with general matter coupling for static black hole solutions is developed with Hamilton-Jacobi approach and new first order sets of equa- tions are presented [1, 2] extending well-known BPS sets [3, 4]. In d = 5 the equations are completely solved for the STU model with constant hypermultiplets and a solution generalizing Maldacena-Nunez black string [4] is found [5]. Then the attention is focused on some integrability properties of minimal gauged super- gravity in d = 4 [6] and Einstein-Maxwell-Lambda system in d dimensions [7]. Always with Hamilton-Jacobi technique, studying the symmetries of the systems the dynamics is solved algebraically for some sets of solutions. For holographic calculations the attractor points deserve particular attention and there- fore I explain their definition for the cases AdS 2 × Σ 2 and AdS 3 × Σ 2 and the calculation of the entropy and the central charge in general matter coupled supergravities. More- over, Freudenthal duality is extended to the abelian gauged case and general matter coupling [8]. The last part is dedicated to the introduction of a solution generating technique based on group theory in FI d = 4 supergravity. Many examples with the simplest prepotentials are shown [9]. With the help of dimensional reduction this solution generating technique is used to produce a rotating black string in d = 5 [5].