Shadow of a rotating braneworld black hole

We investigate the shadow cast by a rotating braneworld black hole, in the Randall-Sundrum scenario. In addition to the angular momentum, the tidal charge term deforms the shape of the shadow. For a given value of the rotation parameter, the presence of a negative tidal charge enlarges the shadow and reduces its deformation with respect to Kerr spacetime, while for a positive charge, the opposite effect is obtained. We also analyze the case in which the combination of the rotation parameter and the tidal charge results in a naked singularity. We discuss the observational prospects corresponding to the supermassive black hole at the Galactic center.

Figure 1

Silhouette of the shadow cast by a black hole situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$, having a rotation parameter $a$ and a tidal charge $Q$. Upper row, left: $a=0$, $Q=-2$ (full line), 0 (dashed-dotted line), 0.5 (dashed line), and $Q_c=1$ (dotted line). Upper row, right: $a=0.5$, $Q=-2$ (full line), 0 (dashed-dotted line), 0.5 (dashed line), and $Q_c=0.75$ (dotted line). Lower row, left: $a=0.9$, $Q=-2$ (full line), 0 (dashed-dotted line), 0.1 (dashed line), and $Q_c=0.19$ (dotted line). Lower row, right: $a=1.1$, $Q=-2$ (full line), $-1$ (dashed-dotted line), $-0.5$ (dashed line), and $Q_c=-0.21$ (dotted line). The shadow corresponds to each curve and the region inside it. All quantities were adimensionalized with the mass of the black hole (see text).

Figure 2

Observables $R_s$ and ${\delta }_s$ as functions of the tidal charge $Q$, corresponding to the shadow of a black hole situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$ and spin parameters $a=0$ (full line), $a=0.5$ (dashed line), $a=0.9$ (dashed-dotted line), and $a=1.1$ (dotted line). The curves with different values of $a$ are not distinguishable in the left plot; a smaller range of $Q$ is shown in the frame inside, in which the different curves can be appreciated.

Figure 3

Contour plots of the observables $R_s$ and ${\delta }_s$ in the plane ($a$, $Q$) for a black hole situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$. Each curve is labeled with the corresponding value of $R_s$ or ${\delta }_s$. The light gray zone represents naked singularities.

Figure 4

Shadow cast by a naked singularity situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$, having a rotation parameter $a$ and a tidal charge $Q$. Upper row, left: $a=0$, $Q=Q_c+{10}^{-5}=1+{10}^{-5}$ (full line), 1.07 (dashed-dotted line), and 1.125 (dashed line). Upper row, right: $a=0.5$, $Q=Q_c+{10}^{-5}=0.75+{10}^{-5}$ (full line), 1 (dashed-dotted line), and 1.2 (dashed line). Lower row, left: $a=0.9$, $Q=Q_c+{10}^{-5}=0.19+{10}^{-5}$ (full line), 0.5 (dashed-dotted line), and 1 (dashed line). Lower row, right: $a=1.1$, $Q=Q_c+{10}^{-5}=-0.21+{10}^{-5}$ (full line), 0.1 (dashed-dotted line), and 1 (dashed line). All quantities were adimensionalized with the mass of the naked singularity (see text).

Figure 5

Observables $R_a$ and ${\phi }_a$ as functions of the tidal charge $Q$, corresponding to the shadow of a naked singularity situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$, and spin parameters $a=0.5$ (dashed line), $a=0.9$ (dashed-dotted line), and $a=1.1$ (dotted line).

Figure 6

Contour plots of the observables $R_a$ (full line) and ${\phi }_a$ (dashed line) in the plane $(a,Q)$ for a naked singularity situated at the origin of coordinates with inclination angle ${\theta }_0=\pi /2$. Each curve is labeled with the corresponding value of $R_a$ or ${\phi }_a$. In the light gray zone, the singularity is covered by the horizon, while in the dark gray zone, the arc is not present due to the absence of the photon sphere.