Thermodynamics of Born-Infeld Black Holes
  We discuss the horizon structure for Born-Infeld black holes, in the context of Einstein-Born-Infeld gravity. We show that the entropy function formalism agrees with a direct calculation of the entropy. With the entropy function formalism we also obtain the entropy when an axion-dilaton system as well as gravitational derivative corrections are included. 
Wissam A. Chemissany, Mees de Roo, Sudhakar Panda