Electromagnetic Energy Extraction in Kerr Black Holes through Frame-Dragging Magnetospheres

• Published in: arXiv.org
• Main Authors: Okamoto, Isao, Uchida, Toshio, Song, Yoogeun
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.10.2024
• Subjects: Angular momentum; Angular velocity; Current sources; Electric fields; Freezing; Magnetospheres
• ISSN: 2331-8422

It is argued that the zero-angular-momentum-observers (ZAMOs) circulating with the frame-dragging-angular-velocity \(\omega\) plays a leading part in energy extraction. When the condition \(\Omega_{\rm F}<\Omega_{\rm H}\) is satisfied, where \(\Omega_{\rm H}\) and \(\Omega_{\rm F}\) are the horizon and field-line (FL) angular-velocities (AVs), they will see that the null surface S\(_{\rm N}\) with \(\omega_{\rm N}=\Omega_{\rm F}\) always exists in the force-free magnetosphere. The pivotal ZAMO-measured FLAV \(\Omega_{\rm ZF} \equiv \Omega_{\rm F} - \omega\) changes sign on this surface S\(_{\rm N}\) where the force-free and freezing-in conditions break down. The force-free magnetosphere is divided on this surface, with particle-current sources on it. The outer domain \({D}_{\rm (out)}\) outside S\(_{\rm N}\) spins forward (\(\Omega_{\rm ZF}>0\)), whereas the inner domain \({D}_{\rm (in)}\) inside spins backward (\(\Omega_{\rm ZF}<0\)). Because the electric field \({\bf E}_{\rm p}\) reverses direction there, the Poynting flux reverses direction as well from outward to inward, though the positive angular momentum always flows outwardly. Electromagnetic self-extraction of energy will be possible only through the frame-dragged magnetosphere, with the inner domain \({D}_{\rm (in)}\) nested between the horizon and the surface S\(_{\rm N}\), when \(\Omega_{\rm F}<\Omega_{\rm H}\) is ensured by the 1st and 2nd laws of thermodynamics.