New non-Abelian black hole solutions in Born-Infeld gravity

We introduce new black hole solutions to the Einstein-Yang-Mills-Born-Infeld (EYMBI), Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet (EYMBIGB) and Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet-Lovelock (EYMBIGBL) gravities in higher dimensions $N\geq 5$ to investigate the roles of Born-Infeld parameter $\beta$. It is shown that, these solutions in the limits of $\beta \to 0,$ and $\beta \to \infty ,$ represent pure gravity and gravity coupled with Yang-Mills fields, respectively. For $0<\beta <\infty$ it yields a variety of black holes, supporting even regular ones at $r=0$.