Extracting Energy from Magnetized Rotating Black Holes in Horndeski Gravity via the Magnetic Penrose Process

Abstract

In Horndeski gravity, we investigate how to extract energy from a rotating black hole immersed in a uniform magnetic field $B$ based on the Magnetic Penrose Process. We map the ergosphere and negative energy regions of this spacetime, and analyze the relationship between the energy extraction efficiency and the hair parameter through both theoretical analysis and numerical simulations. The results show that the larger the hair parameter $h$, the smaller the ergosphere and negative energy regions of the black hole. For the same decay radius, in the case of $\hat{q} B \geq 0$, if the decay radius $r_x > 2$, the efficiency decreases as $h$ increases; if $r_x < 2$, the efficiency increases as $h$ increases; if $r_x = 2$, the efficiency is independent of $h$. However, when $\hat{q}B < 0$, except for the special case $r_x = 2$ where the efficiency is independent of $h$, the variation of efficiency with $h$ depends on the specific values of $r_x$ and $\hat{q}B$, and may exhibit either monotonic decrease or an initial increase followed by a decrease. We also find that in the absence of a magnetic field, the efficiency is negative and meaningless when $r_x > 2$, and such cases are excluded. In addition, when $\hat{q} B \geq 0$, the larger the $h$, the lower the maximum efficiency; when $\hat{q} B < 0$, in the case of a small magnetic field, the efficiency is negative and meaningless, while in the case of a large magnetic field, the efficiency of the black hole with hair is positive at high decay radius and reaches a high value, whereas the efficiency of the Kerr black hole remains negative.

Figures (7)

• Figure 1: The ergosphere region of the black hole for different values of $h$, with $a=0.8$
• Figure 2: $\bar{q}B=0$, $a=0.8$, $\bar{L}=-1$, left panel: $h=1$, red indicates the negative-energy region, blue indicates the ergosphere; right panel: the negative energy region of the particle for different values of $h$
• Figure 3: $\bar{q}B>0$, $a=0.8$, left panel: $h=1$, red indicates the negative energy region, blue indicates the ergosphere; right panel: the negative energy region of the particle for different values of $h$. Top row: $\bar{q}B=0.2$, middle and bottom rows: $\bar{q}B=5$, top and middle rows: $\bar{L}=-1$, bottom row: $\bar{L}=1$
• Figure 4: $\bar{q}B<0.2$, $a=0.8$, $\bar{L}=-10$, left panel: $h=1$, red indicates the negative energy region, blue indicates the ergosphere; right panel: the negative energy region of the particle for different values of $h$. Top row: $\bar{q}B=-0.2$, bottom row: $\bar{q}B=-2$
• Figure 5: $B=0$, the variation of energy extraction efficiency with the decay radius for different values of $h$. The left and right panels show different horizontal axis scales. Upper panel: $a=0.8$, lower panel: $a=0.99$.