Cosmological dynamical black hole solutions

We find new classes of the dynamical black hole solutions in five- or higher-dimensional Einstein–Maxwell-dilaton theory, in which the dilaton field interacts nontrivially with the Maxwell field, and the cosmological constant, with two arbitrary coupling constants. The solutions which are nonstationary, and almost conformally regular everywhere, are constructed by embedding the four-dimensional self-dual geometries. We consider three different situations, where the two coupling constants are not equal, are nonzero equal and finally both are zero. We also consider the cases where one of the metric functions, depends on one coordinate only, and another interesting case where it depends on two spatial coordinates. We also find that the cosmological constant can take all possible negative, zero and positive values, hence our solutions are asymptotically anti-de Sitter, flat and de Sitter. We discuss the properties of the solutions which are the analytic description of coalescing black holes in any dimensions, greater or equal to five.