  Motivated by the recently found 4-dimensional omega-deformed gauge
supergravity, we investigate the black hole solutions within all the single
scalar field consistent truncations of this theory. We construct black hole
solutions that have spherical, toroidal, and hyperbolic horizon topology. The
scalar field is regular everywhere outside the curvature singularity and the
stress-energy tensor satisfies the null energy condition. When the parameter
omega does not vanish, there is a degeneracy in the spectrum of black hole
solutions for boundary conditions that preserve the asymptotic Anti-de Sitter
symmetries. These boundary conditions correspond to multi-trace deformations in
the dual field theory.
