Three dimensional black hole coupled to the Born-Infeld electrodynamics

A nonlinear charged Version of the (2 + I)-anti de Sitter black hole soluti on is derived. The source to the Einstein equations is a Born-Infeld electr omagnetic field, which in the weak field limit becomes the (2 + 1)-Maxwell field. The obtained Einstein-Born-Infeld solution for certain range of the parameters (mass, charge, cosmological and the Born-Infeld constants) repre sent a static circularly symmetric black hole. Although the covariant metri c components and the electric field do not exhibit a singular behavior at r = 0 the curvature invariants are singular at that point. (C) 1999 Publishe d by Elsevier Science B.V. All rights reserved.