We present new results towards the construction of the most general black hole solutions in four-dimensional Fayet-Iliopoulos gauged supergravities. In these theories black holes can be asymptotically AdS and have arbitrary mass, angular momentum, electric and magnetic charges and NUT charge. Furthermore, a wide range of horizon topologies is allowed (compact and noncompact) and the complex scalar fields have a non-trivial radial and angular profile. We construct a large class of solutions in the simplest single scalar model with prepotential F = −iX ⁰ X ¹ and discuss their thermodynamics. Moreover, various approaches and calculational tools for facing this problem with more general prepotentials are presented.

AdS7 supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this pa- per, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS7 a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK scalars. The result signals an instability for all non-supersymmetric solutions except those that have a single D8 on each side. We finally look at non-perturbative instabilities, and find that NS5 bubbles make these remaining solutions decay.

We consider extremal black hole attractors [both Bogomol’nyi-Prasad-Sommerfield (BPS) and non-BPS] for $\mathcal{N}=3$ and $\mathcal{N}=5$ supergravity in $d=4$ space-time dimensions. Attractors for matter-coupled $\mathcal{N}=3$ theory are similar to attractors in $\mathcal{N}=2$ supergravity minimally coupled to Abelian vector multiplets. On the other hand, $\mathcal{N}=5$ attractors are similar to attractors in $\mathcal{N}=4$ pure supergravity, and in such theories only $\frac{1}{\mathcal{N}}$-BPS nondegenerate solutions exist. All the above-mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a $d=5$ uplift. Finally we comment on the duality relations among the attractor solutions of $\mathcal{N}\ge 2$ supergravities sharing the same full bosonic sector.

Supersymmetric black holes in AdS spacetime are inherently interesting for the AdS/CFT correspondence. Within a four dimensional gauged supergravity theory coupled to vector multiplets, the only analytic solutions for regular, supersymmetric, static black holes in AdS₄ are those in the STU-model due to Cacciatori and Klemm. We study a class of U (1)-gauged supergravity theories coupled to vector multiplets which have a cubic prepotential, the scalar manifold is then a very special Kähler manifold. When the resulting very special Kähler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS₄ black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus.