The black hole horizon and the Einstein-Yang-Mills theory

The black hole horizon is a noncommutative region of space-time whose length in the noncommutative case is equal to its length in the commutative case. The horizon's metric is the one associated with the Schwarzschild-Minkowski metric $r$. It is a function of the black hole's average direction in the noncommutative case as well as of the horizon's angle in the commutative case. We study the horizon's metric and compute the angle between the horizon and the horizon's angle as well as the mass of the black hole and the energy of the black hole.