Repetitive Penrose Process in Accelerating Kerr Black Holes

TL;DR

The paper investigates energy extraction from extremal accelerating Kerr black holes via the repetitive Penrose process within the C-metric. It derives the governing equations for energy-momentum exchange, the iterative stopping conditions, and mass/angular-momentum updates under successive decays, and then performs numerical explorations across the acceleration parameter $A$ and decay radius $r_d$. The results show that acceleration enhances energy extraction relative to Kerr, with efficiency exceeding $50 ext{ in cases of small } r_d ext{ and moderate } A$, while large $A$ can drive $E_{extractable}$ toward zero and channel energy into irreducible mass, consistent with a third-law-like constraint. These findings illuminate how acceleration reshapes ergoregion structure and the practical limits of rotational-energy extraction in rotating black-hole spacetimes, with implications for high-energy astrophysical processes.

Abstract

This paper investigates the repetitive Penrose process in accelerating Kerr black holes and explores the influence of the acceleration factor on the repetitive Penrose process. After a brief review of accelerating Kerr black holes, we study the fundamental equations of the Penrose process in this spacetime, examine the stopping conditions required for the repetitive Penrose process, and obtain corresponding numerical results. The conclusions indicate that, apart from the third law of thermodynamics similar to previous cases, accelerating Kerr black holes exhibit stronger energy extraction capabilities compared to Kerr black holes during the repetitive Penrose process. Moreover, in prior studies, the energy utilization efficiency was difficult to exceed $50\%$. However, in accelerating Kerr black holes, when the decay radius is relatively small, the energy utilization efficiency can exceed $50\%$, indicating that the reduced extractable energy primarily transforms into extracted energy rather than irreducible mass. On the other hand, when the initial value of the acceleration factor is large, the extractable energy can decrease to nearly zero, which also differs from the case of Kerr black holes in previous studies.

Figures (4)

• Figure 1: Variation of $E_{extractable}/M$ and $r_{E}/M$ with $\hat{A}$ for an extremal black hole.
• Figure 2: Variation of the lower spin limit with decay radius $\hat{r}_d$ for different $\hat{A}$ values for (a) particle 0, (b) particle 1, and (c) particle 2.
• Figure 3: Comparison of the lower spin limits for the three particles.
• Figure 4: Under different initial $\hat{A}$ values, after the termination of the repetitive Penrose process: (a) the energy return on investment $\xi$; (b, c) the energy utilization efficiency $\Xi$; (d) the extracted energy $E_{extracted}/M_0$; (e) the extractable energy $E_{extractable}/M_0$; (f) the irreducible mass $\frac{M_{irr}}{M_0}$ as functions of the decay radius $\hat{r}_d$. Each oscillation in the curves corresponds to a different number of iterations, caused by the iterative conditions and reflecting the discrete nature of the process.