Non-Supersymmetric Unattractors in Born-Infeld Black Holes

We investigate unattractor behavior in non-extremal black holes in Einstein-Born-Infeld-Dilaton theory of gravity in four-dimensional asymptotically flat spacetime. We obtain solutions which are non-singular near the horizon and dependent on the value of the dilaton field at the infinity, using perturbation method. It is shown that the value of the scalar field at the horizon is determined by its asymptotic value and the charges carried by the black hole. And we also find it is not true in general that the dilaton value at the horizon is a monotonically increasing function of the first coefficient of its series expansion in non-extremal Born-Infeld black holes.