Effects of tidal charge on Blandford-Znajek process around braneworld black holes

Abstract

The Blandford-Znajek (BZ) process is a pivotal mechanism to efficiently extract the energy from a rotating black hole (BH) via its plasma-filled magnetosphere in relativistic astrophysics. Within the framework of extended BZ monopole expansion, we have studied BZ process in the Randall-Sundrum braneworld BH spacetime and analyzed effects of the tidal charge on the energy and angular momentum extraction rates. It is found that the positive tidal charge reduces the BZ power of a braneworld BH, while the negative tidal charge enhances the power. Compared with a Kerr BH of the same mass and angular velocity, the BZ power exhibits a maximum reduction of approximately $15.2\%$ in positive cases, whereas in negative cases, it achieves a maximum enhancement of $66.5\%$ in power output. A similar qualitative trend is also observed for the relative angular momentum extraction rate, albeit with different magnitudes.

Figures (7)

• Figure 1: The $(a,b)$ plane for braneworld BHs. A key feature is that with a negative $b$, it is possible to set $a>M$ without developing any intrinsic singularities. The region below the horizontal dashed line and to the right of the vertical dashed line corresponds to the GR exclusion zone.
• Figure 2: $R_{2}$ versus the dimensionless radial coordinate $w$ for different values of $\beta$. All of the curves seamlessly traverse the static event horizon $w=1$ and run towards zero as $w\to\infty$.
• Figure 3: Plots of $r_{\text{ILS}}^{}$ and $r_{\text{OLS}}^{}$ as functions of the dimensionless spin parameter $\alpha$ for selected values of $\beta$, with $\theta=30^{\circ}$. The right ends of the lines are cut off because for each $\beta$, there exists a physical bound $\sqrt{1-\beta}$ on $\alpha$, as shown in Fig. \ref{['fig:ParaSpace']}. In the left panel, the gray shading delineates the extent of the ergoregion at the same perturbative order as Eq. \ref{['eq:rILS']}.
• Figure 4: Magnetic field lines as the contours of flux $\Psi$ on the $(r,\theta)$ plane for $\alpha=0.7$ (top row), $\alpha=1.0$ (middle row), and $\alpha=1.3$ (bottom row). The leading-order solution \ref{['eq:iniconf']} is also included and depicted with dotted lines. In addition, the gray, red, and purple curves are used to identify the ergosurface, ILS, and OLS, respectively.
• Figure 5: The radial magnetic field $B^{r}=\left(\partial_{\theta}\Psi\right)/\sqrt{-g}$ at the north pole of the braneworld BH horizon. A dashed line defines the boundary of physically acceptable configurations.