  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.
