Black holes with Sol horizon

Many are the ways to evade the topology theorems concerning black holes' horizon; in this
talk I will consider black holes in 5-dimensional N=2 U(1)-gauged supergravity coupled to
vector multiplets, with horizon modelled on solvegeometry, a homogeneous, but anisotropic
space.
Firstly, I will present a solution to the equations of motion for pure gauged
supergravity with magnetic field strength and discuss the thermodynamics of the resulting
solution, which exhibits anisotropic scaling. Furthermore, by means of the Killing spinor
equations, I will illustrate a no-go theorem stating the nonexistence of supersymmetric,
static, electrically or magnetically charged solutions with spatial cross-sections
modelled on solvegeometry. Finally, moving to the attractor mechanism, I will study the
near-horizon geometry of extremal, static black holes with Sol-invariant horizon,
constructing an attractor geometry for purely magnetic field strengths and ruling out its
existence for the electric ones.