Penrose process in magnetized non-Kerr rotating spacetime with anomalous quadrupole moment

TL;DR

This work investigates energy extraction from a non-Kerr rotating spacetime, the Quevedo-Mashhoon metric, in the presence of an external uniform magnetic field. By analyzing charged-particle motion and the negative-energy region with Wald's field, the authors show that a nonzero anomalous quadrupole ${\cal Q}$ can create multi-lobed ergoregions and extend negative-energy regions beyond the ergoregion, while electromagnetic interactions can dramatically boost extraction efficiency. The results reveal that the maximum efficiency $\eta_{\max}$ can exceed 100% in many regimes and may reach extraordinarily large values when the magnetic field is strong enough and the charge-to-mass ratio aligns with the field, with optimal conditions occurring for ${\cal Q}$ positive and $q$ sharing the sign of $B$. These findings offer a theoretical framework for high-energy astrophysical phenomena and provide a potential avenue to test the Kerr hypothesis using magnetic Penrose processes near compact objects.

Abstract

We investigate the magnetic Penrose process in the Quevedo-Mashhoon spacetime, immersed in a uniform magnetic field $B$. This metric is a stationary, axisymmetric, asymptotically flat vacuum solution to Einstein's equations with an arbitrary anomalous quadrupole moment ${\cal Q}$. A non-vanishing ${\cal Q}$ significantly modifies the near-horizon geometry, creating a multi-lobe ergoregion. Both ${\cal Q}$ and $B$ strongly influence the negative-energy region, which can extend well beyond the ergoregion, enabling the magnetic Penrose process to operate far from the ergoregion. Their combined effects allow energy extraction efficiency $η$ to far exceed that of the mechanical Penrose process. The maximum efficiency undergoes three distinct evolutionary stages as ${\cal Q}$ varies. In the absence of the magnetic field, efficiency is optimized for more negative ${\cal Q}$ (yielding a more oblate spacetime than Kerr). When electromagnetic interactions dominate, efficiency peaks when the infalling fragment's charge and $B$ share the same sign and ${\cal Q}$ is more positive (producing a more prolate spacetime than Kerr). These findings support the magnetic Penrose process as a theoretical framework for high-energy cosmic phenomena (e.g., extragalactic high-energy radiation) and as a tool to test the Kerr hypothesis.

Figures (8)

• Figure 1: Shapes of the ergoregion and closed time-like curves (CTCs) region for different ${\cal Q}$. We set $a = 0.8$. For the Kerr case (${\cal Q}=0$) and small $|{\cal Q}|$, there is no CTCs region.
• Figure 2: Shapes of the negative-energy region (NER) and ergoregion for different ${\cal Q}$ with $\bar{q} B=0$. We set $a = 0.8$ and $\ell=-1$. In plotting the NER, the CTCs region has been excluded.
• Figure 3: Shapes of the negative-energy region (NER) and ergoregion for different ${\cal Q}$ with $\bar{q} B >0$. We set $a = 0.8$, and $\ell=-1$ (upper and middle rows), $1$ (bottom row). In plotting the NER, the CTCs region has been excluded.
• Figure 4: Shapes of the negative-energy region (NER) and ergoregion for different ${\cal Q}$ with $\bar{q} B <0$. We set $a = 0.8$ and $\ell=-10$. In plotting the NER, the CTCs region has been excluded.
• Figure 5: Efficiency of energy extraction $\eta$ as a function of the splitting point $r_\ast$ for various ${\cal Q}$ with $B=0$.