Exact solutions of Lovelock-Born-Infeld black holes

The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. It is shown how the conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The differences existing with the Reissner-Nordström black holes are discussed. In particular, we show the existence of charged black holes with a unique horizon.

Figure 1

Comparison between Reissner-Nordström (RN) and $\Psi (r)$ Lovelock-Born-Infeld (LBI) [$\alpha =0.1$, $Q=1$, $\Lambda =0$, $b=1$, $m=\pi$].

Figure 2

Event horizon position (vertical axis) as a function of the black hole mass (horizontal axis) for different values of $b$ (solid curves) and in the Reissner-Nordström case (RN) [$\alpha =0.5$, $Q=3$, $\Lambda =0$].

Figure 3

Graphics of $\Psi (r)$ for different values of $b$, for $m<m_c$: [$m=2$, $\alpha =0.5$, $Q=1$, $b=2$, $\Lambda =0$], for $m=m_c$ [$m=3.49$, $\alpha =0.5$, $Q=1$, $b=2$, $\Lambda =0$] and for $m>m_c$ [$m=5$, $\alpha =0.5$, $Q=1$, $\Lambda =0$].