Solitons and black holes in non-Abelian Einstein–Born–Infeld theory

Recently it was shown that the Born–Infeld modification of the quadratic Yang–Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik–McKinnon solutions obtained within the gravity coupled Yang–Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein–Born–Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born–Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang–Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born–Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violentʹ EYM singularity may be interpreted as a result of non-gravitational quantum effects.