Cosmological rotating black holes in five-dimensional 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 non-trivial 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 black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology. 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 nontrivial "Killing spinor," which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11-dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein type black holes are also discussed.