Gaugings and other aspects in supergravity

Abstract: We discuss various topics in supergravity: gaugings, double field theory and $N=2$ $D=4$ BPS multicenter black holes. We introduce the main features of supergravity, focusing on the aspects of gauged supergravities. We study the embedding-tensor formalism as a tool that facilitates the construction of gauged supergravities due to its covariant formulation as well as its relevance in the description of the magnetic higher-rank field potentials. In particular, we present a full study of the general gaugings of maximal $d=9$ as an example in which this formalism is applied. We obtain all the possible gaugings of the theory and its extended field content. We also classify the orbits of gaugings of maximal and half-maximal $d=9,8,7$ supergravity and study their (non-)geometric origins by means of double field theory. By performing a generalized Scherk-Schwarz dimensional reduction of this T-duality-invariant formalism, we reproduce the orbits found by means of the embedding-tensor formalism. Finally, we study a formalism to describe BPS multicenter solutions for $N=2$, $D=4$ theories with quadratic prepotentials. Based on the charge vector space, this approach allows for the treatment of these solutions in a more general way.