Horizon structure of rotating Einstein-Born-Infeld black holes and shadow

We investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity (beta -> infinity). We find that for a given beta, mass M, and charge Q, there exist a critical spinning parameter a(E) and r(H)(E), which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and aE decreases and r(H)(E) increases with increase of the Born-Infeld parameter beta, while a < a(E) describes a non-extremal Einstein-Born-Infeld black hole with outer and inner horizons. Similarly, the effect of beta on the infinite redshift surface and in turn on the ergo-region is also included. It is well known that a black hole can cast a shadow as an optical appearance due to its strong gravitational field. We also investigate the shadow cast by the both static and rotating Einstein-Born-Infeld black hole and demonstrate that the null geodesic equations can be integrated, which allows us to investigate the shadow cast by a black hole which is found to be a dark zone covered by a circle. Interestingly, the shadow of an Einstein-Born-Infeld black hole is slightly smaller than for the Reissner-Nordstrom black hole, which consists of concentric circles, for different values of the Born-Infeld parameter beta, whose radius decreases with increase of the value of the parameter beta. Finally, we have studied observable distortion parameter for shadow of the rotating Einstein-Born-Infeld black hole.