Minimal surfaces and generalized Einstein–Maxwell-dilaton theory

We present novel classes of nonstationary solutions to the five-dimensional generalized Einstein–Maxwell-dilaton theory with cosmological constant, in which the Maxwell’s field and the cosmological constant couple to the dilaton field. In the first class of solutions, the two nonzero coupling constants are different, while in the second class of solutions, the two coupling constants are equal to each other. We find consistent cosmological solutions with positive, negative or zero cosmological constant, where the cosmological constant depends on the value of one coupling constant in the theory. Moreover, we discuss the physical properties of the five-dimensional solutions and the uniqueness of the solutions in five dimensions by showing the solutions with different coupling constants cannot be uplifted to any Einstein–Maxwell theory in higher dimensions.