  The techniques of spinorial geometry are used to classify solutions admitting
Killing spinors in the theory of minimal anti-de Sitter $N=2$, $D=4$
supergravity, where the gauge kinetic term comes with the opposite sign. There
are four classes of solutions. One class is described by metrics corresponding
to gravitational waves propagating on $AdS_2\times H^2$. The second class of
solution is a new solution corresponding to a special limiting case of the
Killing spinor. The third class of solution corresponds to fibrations over a
Lorentzian three dimensional manifold which has a Lorentzian Gauduchon-Tod
structure. The fourth class of solution is a cosmological extension of a
Majumdar-Papapetrou type solution, described by a function satisfying the wave
equation on $\mathbb{R}^{2,1}$ .

High Energy Physics - Theory