Penrose process in Reissner-Nordström-AdS black hole spacetimes: Black hole energy factories and black hole bombs

Abstract: The Penrose process for the decay of electrically charged particles in a Reissner-Nordstr\"om-anti-de Sitter black hole spacetime is studied. To extract large quantities of energy one needs to mount a recursive Penrose process where particles are confined and can bounce back to suffer ever again a decaying process in the black hole electric ergoregion. In an asymptotically anti-de Sitter (AdS) spacetime, two situations of confinement are possible. One situation uses a reflecting mirror at some radius, which obliges the energetic outgoing particles to return to the decaying point. The other situation uses the natural AdS property that sends back at some intrinsic returning radius those outgoing energetic particles. In addition, besides the conservation laws the decaying process must obey, one has to set conditions at the decaying point for the particles debris. These conditions restrain the possible scenarios, but there are still a great number of available scenarios for the decays. Within these, we choose two scenarios, scenario 1 and scenario 2, that pertain to the masses and electric charges of the final particles. Thus, in the mirror situation we find that scenario 1 leads to a black hole energy factory, and scenario 2 ends in a black hole bomb. In the no mirror situation, i.e., pure Reissner-Nordstr\"om-AdS, scenario 1 leads again to a black hole energy factory, but scenario 2 yields no bomb. This happens because the volume in which the particles are confined increases to infinity along the chain of decays, leading to a zero value of the extracted energy per unit volume and the bomb is demined. The whole treatment performed here involves no backreaction on the black hole mass and electric charge, nevertheless we speculate that the end state of the recursive process is a Reissner-Nordstr\"om-AdS black hole with very short hair, i.e., with one particle at rest at some definite radius.

• The paper demonstrates that the recursive Penrose process in RN-AdS black holes can significantly enhance energy extraction through repeated particle decays.
• It contrasts scenarios using reflecting mirrors with natural AdS confinement to reveal differing outcomes in energy gain and bomb potential.
• The study provides theoretical insights on backreaction and stability, paving the way for future research in black hole thermodynamics and energy applications.

Penrose Process in Reissner-Nordström-AdS Black Hole Spacetimes

The study presented in the paper investigates the Penrose process within Reissner-Nordström-anti-de Sitter (AdS) black hole spacetimes, with a focus on exploring conditions that could render such spacetimes as black hole energy factories or black hole bombs. This analysis is centered around the extraction of energy through a recursive Penrose process, which involves the decay of particles within the electric ergoregion of the black hole. The paper distinguishes between two setups: one where outgoing particles are confined by a reflecting mirror and the other leveraging natural confinement properties of AdS spacetimes.

Theoretical Framework and Methodology

The Penrose process is revisited here in the context of a black hole's electric ergoregion, wherein particles undergo decay such that one resultant particle falls into the black hole with negative energy, boosting the escaping particle's energy beyond the original particle's energy, hence allowing for energy extraction. This mechanism contrasts with the classical understanding that primarily involved Kerr black holes and relied on angular momentum.

In this paper, the recursive nature of the setup is emphasized, wherein the energy extraction process is amplified by the continual bounce-back of particles. By placing reflecting mirrors or taking advantage of the AdS spacetime's reflective properties, particles can repeatedly enter the ergoregion, thus leading to cumulative energy extraction. Two scenarios are primarily examined:

1. Scenario 1: Fine-tuned decay processes ensure that every decay contributes to energy extraction. This scenario is conducive to setting up energy factories where the energy gain is finite but significant.
2. Scenario 2: Over time, and especially with repeated decays, this setup leads to an apparent recession of the outer boundary of confined energy (in the absence of a physical mirror), ultimately yielding potential black hole bombs due to exponential energy growth, although this bomb is demined in the absence of mirrors as energy distribution disperses over an expanding volume.

Numerical and Theoretical Insights

The paper delineates that in the case of a reflective mirror, the volume within which energy density grows remains finite, potentially leading to a bomb scenario depending on the number of recursive iterations. However, without a physical mirror, the negative cosmological constant results in an intrinsic confinement of particles, preventing bomb formation despite infinite energy growth owing to the increased available volume.

Implications and Speculations

For future theoretical explorations, understanding the end state when including backreaction (i.e., the influence of extracted or deposited particles on the black hole's mass and charge) becomes crucial. This recursive process can hint at frameworks where black holes dissipate energy over time, potentially giving rise to exotic states of low-mass, minimally-charged black holes with stable hair configurations.

Conclusion

This study significantly contributes to both theoretical and practical aspects of black hole thermodynamics, potentially indicating pathways for application in telecommunication or energy sectors, through controlled black hole energy extraction. However, it also raises further questions regarding stability, real-time monitoring, and the exact state transitions in black hole physics under such recursive energy extraction models.