Magnetized relativistic accretion disk around a spinning, electrically charged, accelerating black hole: Case of the $C$ metric

This paper examines the general relativistic model of a geometrically thick configuration of an accretion disk around an electrically charged black hole in an accelerated motion, as described by the $C$-metric family. We aim to study effects of the spacetime background on the magnetized version of the thick disk model via the sequences of figures of equilibrium. While maintaining the assumption of non-self-gravitating (test) fluid, we newly explore the influence of the strength of the large-scale magnetic field with field lines organised over the length scale of the black-hole horizon. We systematically analyze the dependence on a very broad parameter space of the adopted scenario. We demonstrate that the $C$ metric can, in principle, be distinguished from Kerr black-hole metric by resolving specific (albeit rather fine) features of the torus, such as the location of its center, inner, and outer rims, and the overall shape. The analytical setup can serve as a test bed for numerical simulations.

Figure 1

Places of horizons as a function of rotation parameter $a$, for different charge parameter $e$.

Figure 2

Allowed parametric regions for the spinning charged $C$ metric as a function of $e$. The regions marked out with hatching correspond to the forbidden regions. The first one represents the result for $a=0$, and the second one represents the result for $a=0.5$.

Figure 3

Allowed parametric regions for the spinning charged $C$ metric as a function of $a$. The regions marked out with hatching correspond to the forbidden regions. The first one represents the result for $e=0$, and the second one represents the result for $e=0.7$.

Figure 4

Plots of metric function $g(\theta )$. The red line corresponds to $g(\theta )=0$, and the hatched region shows $g(\theta )<0$.

Figure 5

Von Zeipel cylinders with respect to the stationary observers. The plots show poloidal sections across the constant $\mathcal{R}$ surfaces, where the circular timelike motion of the fluid is possible. Colors correspond to different values of the radius, as listed on the color bar to the right of each panel. Selected contours are indicated with black lines.

Figure 6

Possible region for having the thick disk model. The dashed curves show when ${\partial }_{\mathrm{r}}W=0$ and ${\partial }_{\theta }W=0$. The dark blue region shows the area where the conditions for a maximum of $W(r,\theta )$ are fulfilled. The white area depicts where the conditions for a minimum of $W(r,\theta )$ are fulfilled.

Figure 7

Contour map of the equipotential surfaces. The red lines show the equipotential corresponding to the inner and outer cusps.

Figure 8

Contour map of the rest-mass density of magnetized disk. The dashed lines point the center of the disk located at $r_c=7.5$. Column 1 shows highly magnetized disk, and column 2 depicts the low-magnetized one.

Figure 9

Contour map of the rest-mass density of highly magnetized disc. The dashed lines point the center of the disk located at $r_c=6.5$.

Figure 10

Contour map of the rest-mass density of highly magnetized disk for various spin values. The dashed lines point the center of the disk. Those solutions have the same parameters ($\alpha$, $L$, and $e$) of the nonrotating solution given at the bottom left of the Fig. 8.