Role of the irreducible mass in repetitive Penrose energy extraction processes in a Kerr black hole

Ruffini R. Bianco C.L. Prakapenia M. Quevedo H. Rueda J.A. Zhang S.
January 2025 American Physical Society

Physical Review Research
2025 #7 Issue 1

The concept of the irreducible mass (Mirr) has led to the mass-energy (M) formula of a Kerr black hole (BH), in turn leading to its surface area S=16πMirr2. This also allowed the coeval identification of the reversible and irreversible transformations, soon followed by the concepts of extracted and extractable energy. This new conceptual framework avoids inconsistencies recently evidenced in a repetitive Penrose process. We consider repetitive decays in the ergosphere of an initially extreme Kerr BH and show the processes are highly irreversible. For each decay, the particle that the BH captures causes an increase of the irreducible mass (so the BH horizon), much larger than the extracted energy. The energy extraction process stops when the BH reaches a positive spin lower limit set by the process boundary conditions. Thus, the reaching of a final nonrotating Schwarzschild BH state through this accretion process is impossible. We have assessed such processes for selected decay radii and incoming particle with rest mass 1% of the BH initial mass M0. For r=1.2M and 1.9M, the sequence stops after 8 and 34 decays, respectively, at a spin 0.991 and 0.857, the energy extracted has been only 1.16%, and 0.42%, the extractable energy is reduced by 17% and 56%, and the irreducible mass increases by 5% and 22%, all values in units of M0. These results show the highly nonlinear change of the BH parameters, dictated by the BH mass-energy formula, and that the BH rotational energy is mainly converted into irreducible mass. Thus, evaluating the irreducible mass increase in any energy extraction processes in the Kerr BH ergosphere is mandatory.

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ICRA, Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, Rome, I-00185, Italy
INAF, Viale del Parco Mellini 84, Rome, I-00136, Italy
INAF, Istituto di Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere 100, Rome, I-00133, Italy
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, Mexico City, 04510, Mexico
Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Almaty, 050040, Kazakhstan
ICRANet-Ferrara, Dipartimento di Fisica e Scienze della Terra, Università Degli Studi di Ferrara, Via Saragat 1, Ferrara, I-44122, Italy
Dipartimento di Fisica e Scienze della Terra, Università Degli Studi di Ferrara, Via Saragat 1, Ferrara, I-44122, Italy
School of Astronomy and Space Science, University of Science and Technology of China, Hefei, 230026, China
CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, 230026, China

ICRANet
ICRANet
ICRA
INAF
INAF
Instituto de Ciencias Nucleares
Al-Farabi Kazakh National University
ICRANet-Ferrara
Dipartimento di Fisica e Scienze della Terra
School of Astronomy and Space Science
CAS Key Laboratory for Research in Galaxies and Cosmology

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