Figure 1

Part (a) shows the relation among the Sen, Gibbons-Maeda (GM), and Kerr solutions, and the boundaries separating the solutions into black hole solutions and naked singular solutions. The curve denoted by extreme corresponds to the extreme black hole, while the small semicircle at $Q=\sqrt{2}M$ corresponds to a naked singularity. Part (b) represents the relation among the Kerr-Newman (KN), Reissner-Nordström (RN), and Kerr solutions, and the boundaries separating the solutions into black hole solutions and naked singular solutions.Reuse & Permissions

Figure 2

Parts (a) and (b) show the capture regions in the impact parameter space $(b_x,b_y)$ for the GM black holes (BHs). Part (c) shows that for the GM naked singularity (NS). The unit of the coordinates is the mass $M_{\mathrm{GM}}$ in all cases. In the cases of black hole, (a) and (b), the photons are captured both by the circular photon orbit and event horizon to form the disks in the impact parameter space, while in the naked singularity case, (c), only the principal null geodesic is captured to form the dot.Reuse & Permissions

Figure 3

Part (a) shows the capture region by the GM black hole. Part (b) shows the capture region by the RN naked singularity with the same extremality as the GM in (a). The unit of the coordinates is the mass $M_{\mathrm{GM}}$ and $M_{\mathrm{RN}}$, respectively. In the case of (a), the capture region forms the disk. While in the case of (b), the capture “region” is just the one-dimensional circle with the dot. This difference stems from the (non)existence of the event horizon (see also Table. ).Reuse & Permissions

Figure 4

Potentials for the GM black hole, (a), those for the GM naked singularity, (b), and those for the RN naked singularity, (c). See Figs. 2a, 2c, 3b for the corresponding shadows, respectively. (a) The solid curve represents the potential for the unstable circular photon orbit, which forms the boundary of the shadow. The dotted curve represents the potential for the null geodesic forming the inner region of shadow. The dashed curve represents the potential for the null geodesic scattered away, which has a turning point outside the event horizon (normalized to being located at $r=2$). (b) The dotted curve represents the potential for the principal null geodesic, which forms the dot in the shadow. While the potential for the null geodesic which is scattered away is plotted by the dashed curve. (c) The dotted (solid) curve represents the potential for the principal null geodesic (marginally stable circular photon orbit), which forms the dot (circle) in the shadow. The dashed (dot-dashed) curve represents the potential for the null geodesic corresponding to the outer (inner) region of the circle in the shadow.Reuse & Permissions

Figure 5

Comparison of the shapes of the capture region among various charges for the Sen black hole. The angular momentum and inclination angle are common for all cases, $J/M^2=1/2$ and $i=\pi /2$. The unit of the coordinates is the mass $M$. One sees that the capture region deviates from a round disk as the charge increases.Reuse & Permissions

Figure 6

Comparison of the shapes of the capture region between the Sen black hole, (a), and the Kerr-Newman naked singularity, (b), with the common parameters $Q/M=Q_{\mathrm{KN}}/M_{\mathrm{KN}}=1$, $J/M^2=J_{\mathrm{KN}}/M_{\mathrm{KN}}^2=1/2$, and $i=\pi /6$. The capture region in (a) is a deformed disk. While the capture region in (b) is an arc with a small deformed disk. The arc part is formed by the circular photon orbits located at $r>0$, while the boundary of the small deformed disk is formed by the unstable circular photon orbits located at $r<0$.Reuse & Permissions