2 8 A pr 2 00 7 Scalar - tensor black holes coupled to Born - Infeld nonlinear electrodynamics

The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The noscalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.