Rotating black holes in fake supergravity

In recent series of papers, we found an arbitrary dimensional, time-evolving and spatially-inhomogeneous solutions in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric charged black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lematre- Robertson-Walker (FLRW) universe. We discuss in this paper that in 5-dimensions this equilibrium condition traces back to the 1st-order Killing spinor equation in fake supergravity coupled to arbitrary U(1) gauge fields and scalars. We present a 5-dimensional, asymptotically FLRW, rotating black-hole solution admitting a non- Trivial Killing spinor, which is a spinning generalization of our previous solution. We discuss physical properties and causal structures of solutions with nonvanishing angular momentum.