SUPERGRAVITY BLACK HOLE AND BRANE SOLUTIONS IN VARIOUS DIMENSIONS

Black holes and branes, supergravity solutions and BPS states, they all play a fundamental role in the understanding of quantum theories of gravity; in this thesis we investigate some of their features from different perspectives. We start considering 4-dimensional N=2 FI-gauged supergravity and construct BPS rotating black holes for the CP^n and t^3 models. Moreover, we obtain a non-extremal generalization of the former and study its thermodynamics. Then, we move to D=5 and search for static solutions with solvegeometry cross-sections. The result is a magnetically charged black hole solution of pure gauged supergravity, a magnetic attractor for the general theory and a no-go theorem ruling out the existence of static, non-dyonic, supersymmetric spacetimes with solvegeometry cross-sections. Subsequently, we focus on M-theory and type-IIA backgrounds that exhibit an AdS3 factor. We obtain the brane set-ups giving rise to these solutions and provide a defect interpretation of the dual 2d CFTs as surface defects within higher-dimensional CFTs. Moreover, we construct a new solution to type-IIA supergravity preserving (0,4) supersymmetries. Finally, we analyze four- and three-charge black holes in heterotic string theory--consisting of bound states of strings, NS5-branes and, optionally, a Kaluza-Klein monopole--and derive an $alpha'$-exact expression for the shift that the conserved charges suffer due to the inclusion of higher-curvature terms. To this end, we apply both the Wald entropy formula and the entropy function formalism.