On horizons and wormholes in k-essence theories

We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F ( X ), X ≡ ϕ , α ϕ , α . A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F ( X ) is required to have a finite derivative dF/dX . Two exact solutions are obtained for special cases of kessence: one for F ( X ) = F 0 X 1/3 , another for F ( X ) = F 0 | X | 1/2 − 2Λ, where F 0 and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained nogo theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.