Horizon structure of rotating Einstein–Born–Infeld black holes and shadow
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 ( $$\beta \rightarrow \infty $$ ). 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 $$a_{E}$$ 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.