Topological Black Holes of Einstein-Yang-Mills dilaton Gravity

Understand

We present the topological solutions of Einstein-dilaton gravity in the presence of a non-Abelian Yang-Mills field.

• In 4 dimensions, we consider the $So(3)$ and $So(2,1)$ semisimple group as the Yang-Mills gauge group, and introduce the black hole solutions with spherical and hyperbolic horizons, respectively.
• The solution in the absence of dilaton potential is asymptotically flat and exists only with spherical horizon.
• Contrary to the non-extreme Reissner-Nordstrom black hole, which has two horizons with a timelike and avoidable singularity, here the solution may present a black hole with a null and unavoidable singularity with only one horizon.