Penrose process in radiating Kerr-Vaidya black holes: efficiency, energy transport, and the viability boundary
Abstract
We study single-particle Penrose extraction from a rotating black hole whose mass decreases in time, described by the ingoing Kerr-Vaidya metric, imposing exact four-momentum conservation at the decay. We prove that the local efficiency is bounded by the instantaneous Kerr value, through a covariant bound that reduces to the Bardeen-Press-Teukolsky limit at the horizon, and we derive an exact transport law, dE/dtau = -dm/dt (r/Sigma) p_r^2 for fixed spin parameter, by which every timelike geodesic gains energy while the hole loses mass. The net energy gain therefore splits into a local Penrose term and two transport terms, which we compute numerically as functions of spin and mass-loss rate for two mass-loss laws. With fixed spin parameter, extraction is possible only below a critical rate alpha_crit(a) = (M-a)/Delta v, set by the approach of the hole to extremality; with fixed a/m no such boundary exists. The transport law extends to the Kerr-Newman-Vaidya family, and the regime where the dynamics matter is shown to lie far outside astrophysical mass-loss rates.
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BibTeX
@misc{buffoli2026penrose,
title = {{Penrose process in radiating Kerr-Vaidya black holes: efficiency, energy transport, and the viability boundary}},
author = {Fabio Buffoli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.19175},
eprint = {2609.19175},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19175},
}
RIS
TY - UNPB
TI - Penrose process in radiating Kerr-Vaidya black holes: efficiency, energy transport, and the viability boundary
AU - Fabio Buffoli
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.19175
UR - https://arxiv.org/abs/2609.19175
AB - We study single-particle Penrose extraction from a rotating black hole whose mass decreases in time, described by the ingoing Kerr-Vaidya metric, imposing exact four-momentum conservation at the decay. We prove that the local efficiency is bounded by the instantaneous Kerr value, through a covariant bound that reduces to the Bardeen-Press-Teukolsky limit at the horizon, and we derive an exact transport law, dE/dtau = -dm/dt (r/Sigma) p_r^2 for fixed spin parameter, by which every timelike geodesic gains energy while the hole loses mass. The net energy gain therefore splits into a local Penrose term and two transport terms, which we compute numerically as functions of spin and mass-loss rate for two mass-loss laws. With fixed spin parameter, extraction is possible only below a critical rate alpha_crit(a) = (M-a)/Delta v, set by the approach of the hole to extremality; with fixed a/m no such boundary exists. The transport law extends to the Kerr-Newman-Vaidya family, and the regime where the dynamics matter is shown to lie far outside astrophysical mass-loss rates.
ER -