Black hole solutions coupled to Born–Infeld electrodynamics with derivative corrections

We investigate black hole solutions in the Einstein–Born–Infeld system. We clarify the role played by derivative corrections to the Born–Infeld (BI) action. The qualitative differences from the case without derivative corrections are: (i) there is no particlelike solution, (ii) the existence of the inner horizon is restricted to the near extreme solutions, and (iii) the contribution of the BI parameter b to the gravitational mass and the Hawking temperature works in the opposite direction.