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

TL;DR

This paper studies how energy can be extracted from rotating black holes in Horndeski gravity using the Magnetic Penrose Process, analyzing the effects of the hair parameter and magnetic field on efficiency.

Contribution

It provides a detailed analysis of energy extraction efficiency in Horndeski gravity black holes, highlighting the influence of the hair parameter and magnetic field through theoretical and numerical methods.

Findings

Larger hair parameter reduces ergosphere and negative energy regions.

Efficiency varies with hair parameter, magnetic field, and decay radius, showing complex dependencies.

Without magnetic field, efficiency is negative and meaningless for certain radii.

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.