Energy extraction via magnetic reconnection in Konoplya-Rezzolla-Zhidenko parametrized black holes

Recently, Comisso and Asenjo proposed a novel mechanism for harnessing energy from black holes through magnetic reconnection. Our study focuses on exploring the utilization of this mechanism on Konoplya-Rezzolla-Zhidenko (KRZ) parametrized black holes to assess the impact of deformation parameters on energy extraction. Among the various parameters, $\{{\delta }_1,{\delta }_2\}$ are identified as the most important factors affecting the physics under consideration. The influence of these two parameters on the ergoregion, circular geodesics in the equatorial plane, and energy extraction from the KRZ black holes through magnetic reconnection is carefully analyzed. Results indicate that deviations from the Kerr metric have a notable influence on the energy extraction process. Particularly, energy extraction is enhanced with more negative ${\delta }_1$ or more positive ${\delta }_2$ within the range constrained by current astronomical observations, resulting in significantly higher maximum power and efficiency compared to the Kerr model. Moreover, when ${\delta }_2$ is sufficiently negative, extracting energy through this mechanism becomes increasingly challenging, necessitating an exceptionally high black hole spin.

Figure 1

Ergosphere in the equatorial plane $r=r_{\mathrm{sl}}$ as a function of $\{{\delta }_1,{\delta }_2\}$ for various $a$. The event horizon in the equatorial plane is located at $r=r_0=1+\sqrt{1-a^2}$. In the left panel ${\delta }_2=0$, while in the right panel ${\delta }_1=0$.

Figure 2

Radius of innermost stable circular orbit as a function of the spin $a$. Here, we fix ${\delta }_2=0$ and study the influence of ${\delta }_1$. The Kerr case $({\delta }_1={\delta }_2=0)$ is also shown for comparison. $r_{\mathrm{ISCO}}^{+}$ and $r_{\mathrm{ISCO}}^{-}$ represent the corotating and counter-rotating orbits, respectively. $r_0$ is the event horizon and $r_{\mathrm{sl}}$ is the ergosphere.

Figure 3

Radius of innermost stable circular orbit as a function of the spin $a$. Here we fix ${\delta }_1=0$ and study the influence of ${\delta }_2$. $r_{\mathrm{ISCO}}^{+}$ and $r_{\mathrm{ISCO}}^{-}$ represent the corotating and counter-rotating orbits, respectively. $r_0$ is the event horizon and $r_{\mathrm{sl}}$ is the ergosphere.

Figure 4

The energy-at-infinity density ${\epsilon }_{\pm }^{\infty }$ as a function of the orientation angle $\xi$ (top panels) and the plasma magnetization ${\sigma }_0$ (bottom panels) for various ${\delta }_1$ and ${\delta }_2$, with $a=0.99$ and $r_X=r_{\mathrm{ISCO}}^{+}$. In the top panels, we set ${\sigma }_0=10$, while in the bottom panels, we set $\xi =0$. In the left panels ${\delta }_2=0$, while in the right panels ${\delta }_1=0$. Solid curves are ${\epsilon }_{+}^{\infty }$ while dashed ones are ${\epsilon }_{-}^{\infty }$.

Figure 5

Permissible regions (shaded) in $a–r_X$ plane where the energy extraction conditions are satisfied for $r_{\mathrm{ISCO}}^{+}\le r_X<r_{\mathrm{sl}}$. We set $\xi =\frac{\pi }{12}$ and ${\sigma }_0=10$. In the left panels ${\delta }_2=0$, while in the right panels ${\delta }_1=0$.

Figure 6

${\mathcal{P}}_{\mathrm{extr}}$ as a function of the X-point location $r_X$ for various $\{{\delta }_1,{\delta }_2\}$, with $\xi =\frac{\pi }{12},{\sigma }_0=10$ and $U_{\mathrm{in}}=0.1$. $r_X$ is restricted to be in the range $r_{\mathrm{ISCO}}^{+}\le r_X<r_{\mathrm{sl}}$. In the left panels ${\delta }_2=0$, while in the right panels ${\delta }_1=0$.

Figure 7

$\eta$ as a function of the X-point location $r_X$ for various $\{{\delta }_1,{\delta }_2\}$, with $\xi =\frac{\pi }{12},{\sigma }_0=10$ and $U_{\mathrm{in}}=0.1$. $r_X$ is restricted to be in the range $r_{\mathrm{ISCO}}^{+}\le r_X<r_{\mathrm{sl}}$. In the left panels ${\delta }_2=0$, while in the right panels ${\delta }_1=0$.