Black holes in an expanding universe from fake supergravity

In arXiv:0902.4814, a general recipe to construct fake supersymmetric solutions to fake N = 2, d = 4 gauged supergravity coupled to abelian vector multiplets was presented. We use these results to find new multi-centered black hole solutions in an asymptotically FLRW universe. These satisfy the weak energy condition and are maximally charged under two U(1) gauge fields coupled to a scalar, which drives the cosmic expansion while rolling down its potential. As a special subcase, our black holes include the ones constructed previously by Gibbons and Maeda in arXiv:0912.2809. The latter contain two non-negative real numbers n(S), n(T) obeying the constraint n(S) + n(T) = 4, with the cases n(T) = 4 and n(T) = 1 corresponding to the Kastor-Traschen and the Maeda-Ohta-Uzawa solution respectively. We show that n(S), n(T) arise directly as exponents in the prepotential of the fake supergravity theory, and that the above constraint stems from the fact that the prepotential must be a homogeneous function of degree two. Finally, some physical properties of the black holes, like asymptotic behaviour, curvature singularities and trapping horizons, are also discussed. Similar to other solutions that appeared previously in the literature, there is a symmetry enhancement near the event horizon, which becomes therefore a Killing horizon, in spite of the highly dynamical nature of the original spacetime. The temperature associated to this Killing horizon turns out to be nonvanishing.