Cosmological rotating black holes in five-dimensional fake supergravity

Abstract

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution 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 black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order ``Killing spinor'' equation in ``fake supergravity'' coupled to arbitrary $U(1)$ gauge fields and scalars. We present a five-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.