Test particle motion in the Born-Infeld black hole

In this paper, we review the classification of the orbits followed by charged massive test particles in the gravitational background of the black hole solutions of Einstein-Born-Infeld spacetime. Even though some features are quite similar to those of Reissner-Nordström spacetime, there are also important differences, particularly those related to the effective potential governing the orbital motion. Explicit solutions involving Weierstrass functions are given for a pair of specific scenarios.

Figure 1

The mass $M$ of the EBI black hole as a function of $r$ ($Q=2,b=5$); at $M=0.7$ there is only one horizon.

Figure 2

The mass $M_{ex}$ of the extreme EBI black hole as a function of $b$.

Figure 3

Distribution of roots of the function $R$ on the $k-E$ plane showing the transition from Schwarzschild spacetime ($\tilde{b}=1\times {10}^{-6}$, solid line) to RN spacetime ($\tilde{b}=1\times {10}^6$, dashed line); the regions with 4 zeroes are not indicated.

Figure 4

$\tilde{Q}=0.4$, $\tilde{G}=0.25$, $\tilde{q}=0.05$, $\tilde{g}=0.1$, $k=4$.

Figure 5

$\tilde{Q}=0.4$, $\tilde{G}=0.25$, $\tilde{q}=-4$, $\tilde{g}=0.1$, $k=0.2$.

Figure 6

$\tilde{Q}=0.4$, $\tilde{G}=0.25$, $\tilde{q}=4$, $\tilde{g}=0.1$, $k=0.2$.

Figure 7

$\tilde{Q}=0.4$, $\tilde{G}=0.25$, $\tilde{q}=0.025$, $\tilde{g}=0.1$, $k=2.7$.

Figure 8

The function ${\tilde{\mathrm{\Delta }}}_r$ for different values of the dimensionless parameter $\tilde{b}=r_s^{2}b$; the solid line corresponds to the RN spacetime with $\tilde{Q}=\sqrt{0.2}$.