Non-Existence of Black Holes with Non-Canonical Scalar Fields

We study the existence of stationary black holes with a non-canonical scalar field as a matter source. We prove a simple black hole no-hair theorem which rules out the existence of asymptotically flat black holes which are static or stationary and axisymmetric possessing scalar hair for a wide class of non-canonical scalar field theories. This applies to scalar field theories which are of the form of K-essence theories. In particular, we rule out the existence of such black holes in the ghost condensate model, and in large sectors of the Dirac-Born-Infeld model.