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 $N\ge 5$ 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 $r=0$.

Figure 1

Plots of $f(r)$ versus $r$, for $M=1$, $Q=1$, $\Lambda =0$ and $\beta =0$, 0.1, 0.5, 1.0, 10, 1000, and $\infty$. The role of $\beta$ may be interpreted as an adjustment key to get any value for the radius of the horizon, between the extremal horizons of the corresponding pure gravity (E) ($\beta =0$) and EYM ($\beta =\infty$) black holes.

Figure 2

Plots of $f_{-}(r)$ versus $r$, for $M=1$, $Q=1$, $\Lambda =0$ and $\beta =0$, 0.1, 0.5, 1.0, 10, 50, and $\infty$. The role of $\beta$ may be interpreted as a regulator to get any value for the radius of the horizon, between the horizons corresponding to pure gravity with a GB term (EGB) ($\beta =0$) and EYMGB ($\beta =\infty$) black holes. The smaller figure shows that by the choice of $\beta$ it is possible to obtain black holes which are regular at $r=0$.

Figure 3

Plots of $f(r)$ versus $r$, for fixed values of $M=1$, $Q=1$, $\Lambda =0$, ${\alpha }_2=1/12$, ${\alpha }_3=1/72$, and $\beta =0$, 0.01, 0.1, 1, 10, 100, 1000, and $\infty$. Different values of $\beta$ from 0 to $\infty$, correspond to different black hole solutions between EGBL gravity and EYMBIGBL. By setting $\Lambda =0$, the metric function represents an A-F black hole and therefore independent of $\beta$, all cases converge to a constant $(=1)$.

Figure 4

Plots of $f(r)$ versus $r$, for fixed values of $M=1$, $Q=1$, $\Lambda =0.3$, ${\alpha }_2=1/12$, ${\alpha }_3=1/72$, and $\beta =0$, 0.01, 0.1, 1, 10, 100, 1000, and $\infty$. Different values of $\beta$ from 0 to $\infty$, correspond to different black hole solutions between EGBL gravity and EYMBIGBL. By setting $\Lambda =0.3$, the metric function represents an AdS black hole and therefore independent of $\beta$, all cases diverge to a $-\infty$.