Eur. Phys. J. C (2016) 76: 273
https://doi.org/10.1140/epjc/s10052-016-4122-9

Regular Article - Theoretical Physics

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

¹ Institute of Nuclear Physics, Ulughbek, Tashkent, 100214, Uzbekistan
² Inha University in Tashkent, Tashkent, 100170, Uzbekistan
³ Ulugh Beg Astronomical Institute, Astronomicheskaya 33, Tashkent, 100052, Uzbekistan
⁴ National University of Uzbekistan, Tashkent, 100174, Uzbekistan
⁵ Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, 110025, India
⁶ Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of Kwa-Zulu-Natal, Private Bag 54001, Durban, 4000, South Africa

^* e-mail: farruh@astrin.uz
^** e-mail: fatamurotov@gmail.com

Received: 15 June 2015
Accepted: 1 May 2016
Published online: 17 May 2016

Abstract

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 (). We find that for a given , mass M, and charge Q, there exist a critical spinning parameter and , which corresponds to an extremal Einstein–Born–Infeld black hole with degenerate horizons, and decreases and increases with increase of the Born–Infeld parameter , while describes a non-extremal Einstein–Born–Infeld black hole with outer and inner horizons. Similarly, the effect of 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 , whose radius decreases with increase of the value of the parameter . Finally, we have studied observable distortion parameter for shadow of the rotating Einstein–Born–Infeld black hole.