Energy extraction via magnetic reconnection in magnetized black holes
Shao-Jun Zhang
Abstract and summary · read the original at the source
In one page
Shao-Jun Zhang takes a recent and very attractive idea — that you can pull energy out of a spinning black hole by letting the magnetic field in the plasma around it snap and reconnect, which is the Comisso-Asenjo mechanism — and asks what happens when the magnetic field is strong enough to bend spacetime itself. Earlier treatments let the field ride on a fixed Kerr geometry. Zhang instead uses the Kerr-Melvin metric, an exact solution for a rotating black hole sitting in a uniform magnetic field, so the field pushes back on the geometry it lives in. Two things follow. A stronger field magnetises the plasma better, which helps extraction; but the same field shrinks the ergoregion where the reconnection has to happen, which hurts it. The two effects cross, so there is an optimum field strength rather than more-is-better. And above a critical strength, set by the hole’s spin, circular orbits in the equatorial plane stop existing at all.
Why it matters hereChapter 6 is about drawing usable energy out of the structure of a field rather than out of fuel, and this is that argument at astrophysical scale: the reservoir is a spinning hole’s rotation, the tap is a reconnecting current sheet, and the paper does the honest engineering of finding where the tap works best. Chapter 13 gets the point that matters most for the site’s picture — a magnetic field strong enough to do work is also strong enough to change the metric it sits in, so field engineering and spacetime engineering stop being separate subjects.
What it claims
01The Kerr-Melvin metric, an exact stationary axisymmetric electrovacuum solution for a rotating black hole immersed in a uniform magnetic field, is used as the local near-horizon geometry so that the magnetic field’s backreaction on spacetime is carried through the whole calculation rather than assumed away.Section II, Equations 1 to 3
Published and peer-reviewed02The event horizon is unmoved by the field, but the ergosphere is not: at fixed spin, a larger magnetic field shrinks the equatorial ergoregion, which is exactly the region in which the reconnection has to take place.Section II, Equations 4 and 5, Figure 1
Published and peer-reviewed03There is a critical field strength above which circular orbits in the equatorial plane cease to exist. That critical value rises with the hole’s spin, and in the extreme limit of maximal spin it approaches about 0.57 in the paper’s units, so a field above that shuts the mechanism down in this scenario.Section III, Figure 2; Section V, Summary and Conclusions
Published and peer-reviewed04Both the extracted power per unit enthalpy and the extraction efficiency first rise and then fall as the magnetic field grows, so a moderate field strength is the most conducive to energy extraction rather than the strongest available field.Section IV B, Equations 20 and 21, Figures 6 and 7
Published and peer-reviewed05Including the backreaction always lowers the yield relative to the pure Kerr treatment: for a spin of 0.99 the maximum power in the Kerr-Melvin case falls to roughly 95, 93, 74 and 47 percent of the Kerr value as the field is raised through 0.05, 0.1, 0.2 and 0.3, while the efficiency ratio falls only from about 99.8 to 94.0 percent over the same range.Section IV B, text accompanying Figures 6 and 7
Published and peer-reviewed06The author names the next steps himself: extraction may still work on elliptic or non-equatorial orbits outside the case treated here, realistic astrophysical settings need full relativistic magnetohydrodynamics rather than this simplified model, and quantum effects must enter once the field approaches the Schwinger critical field of about 4.4 times ten to the thirteenth gauss.Section V, Summary and Conclusions, final three paragraphs and footnote 1
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Read it · abstract
Abstract
The Comisso-Asenjo mechanism is a novel mechanism proposed recently to extract energy from black holes through magnetic reconnection of the surrounding charged plasma, in which the magnetic field plays a crucial role. In this work, we revisit this process by taking into account the backreaction of the magnetic field on the black hole's geometry. We employ the Kerr-Melvin metric to describe the local near-horizon geometry of the magnetized black hole. By analyzing the circular orbits in the equatorial plane, energy extraction conditions, power and efficiency of the energy extraction, we found that while a stronger magnetic field can enhance plasma magnetization and aid energy extraction, its backreaction on the spacetime may hinder the process, with a larger magnetic field posing a greater obstacle. Balancing these effects, an optimal moderate magnetic field strength is found to be most conducive to energy extraction. Moreover, there is a maximum limit to the magnetic field strength associated with the black hole's spin, beyond which circular orbits in the equatorial plane are prohibited, thereby impeding energy extraction in the current scenario.
Shao-Jun Zhang, Energy extraction via magnetic reconnection in magnetized black holes, Journal of Cosmology and Astroparticle Physics 2024(07), 042; author preprint arXiv:2405.16941v3, 18 July 2024. Institute for Theoretical Physics and Cosmology, and United Center for Gravitational Wave Physics, Zhejiang University of Technology, Hangzhou.
(Abstract only — see the rights note above for why the published text is not reproduced here; the author’s preprint is free to read on arXiv. On this site, the field science this calculation rests on is surveyed in Magnetic Reconnection in the Space Sciences: Past, Present, and Future. The horizon-physics companions are Experimental Black-Hole Evaporation? and Partner particles for moving mirror radiation and black hole evaporation. For the older energy-extraction routes this mechanism is measured against — the Penrose process and its descendants — see The generalized second law implies a quantum singularity theorem, Rotating traversable wormholes and Null energy conditions in quantum field theory.)
The way in
https://doi.org/10.1088/1475-7516/2024/07/042LICENCE CHECKED, NOT PROMOTED. Published as Journal of Cosmology and Astroparticle Physics 2024(07), 042, by IOP Publishing on behalf of SISSA; the IOP record carries only the standard copyright and text-and-data-mining pages, with no Creative Commons statement, so no text of the published article is reproduced here. The author’s own preprint is free to read as arXiv:2405.16941v3 (18 July 2024) under the arXiv.org perpetual non-exclusive licence, which permits distribution by arXiv but is not an open licence this site can re-publish under. The abstract below is the author’s own, as posted on arXiv and as deposited with Crossref by IOP; the summary and every claim locator below were read from the full preprint text. Author affiliation: Institute for Theoretical Physics and Cosmology, and United Center for Gravitational Wave Physics, Zhejiang University of Technology, Hangzhou. Supported by the National Natural Science Foundation of China, grant 12075207.
How to cite it
Shao-Jun Zhang (2024) Energy extraction via magnetic reconnection in magnetized black holes. doi:10.1088/1475-7516/2024/07/042
Where it sits in the curriculum
Plasmoids, charge clusters and the orbsThe vacuum at cosmic scale