Hairy mass bound in the Einstein-Born-Infeld black hole

Abstract: We study the Einstein-Born-Infeld (EBI) theory where the hairy black hole was found as the EBI black hole by using Hod's idea. The hair extends beyond the photon-sphere of the EBI black hole spacetimes. We show that the region beyond the photon-sphere involves more than half of the total hair's mass, which respects Hod's conjectured bound.