发表机构
International Center for Relativistic Astrophysics Network (ICRANet); Université Libre de Bruxelles; International Solvay Institutes（国际相对论天体物理网络; 布鲁塞尔自由大学; 国际索尔维研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了磁化零视界不可约质量的通用平衡方程，并应用于Wang的Blandford-Znajek引擎，揭示旋转功的一半不可逆地增加视界面积，另一半转化为电磁功率。
AI 中文摘要
我们从一个一般性问题开始：当视界不是平稳时，磁化黑洞的不可约质量如何变化？零Raychaudhuri方程对任何光滑的零视界给出了精确的面积平衡，而不假设平稳性或轴对称性。当视界是轴对称的并允许可积的准局部哈密顿量时，这一几何恒等式变为能量平衡。该方程将面积增长、旋转和电磁功、非平稳聚焦、正则通量修正以及内部边界项分开处理。然后我们转向Wang的自引力分裂单极Blandford-Znajek引擎。在弱场和慢旋转区域，P/M_H≪1且a/M_H≪1，我们的通用平衡重现了Wang的质量和角动量损失率。不可约质量M_irr=√(A_H/(16π))揭示了这些速率本身所不能显示的内容。它衡量了视界不可逆吸收的旋转功部分。在固定磁通量和阻抗匹配条件下，瞬时旋转功的一半以电磁功率形式离开。另一半增加了视界面积和M_irr。这一简化背后的假设被明确推导出来。一个最小的无耗散世界体积作用使电流片贡献在O(p^2ε^2)阶消失。对Wang的微扰场进行直接幂次计数，结合兼容的正则通量规定，给出了O(p^2)+O(ε^2)的相对聚焦和正则修正。这些估计标定了简化Blandford-Znajek轨迹保持可控的范围。将该轨迹扩展到高自旋需要额外的外推。将准局部视界损失与无穷远处测量的能量联系起来需要单独计算渐近通量。
英文摘要
We begin with a general question: how does the irreducible mass of a magnetized black hole change when the horizon is not stationary? The null Raychaudhuri equation gives an exact area balance for any smooth null horizon, without assuming stationarity or axisymmetry. When the horizon is axisymmetric and admits an integrable quasilocal Hamiltonian, this geometrical identity becomes an energy balance. The equation keeps area growth, rotational and electromagnetic work, nonstationary focusing, canonical-flux corrections, and internal-boundary terms separate. We then turn to Wang's self-gravitating split-monopole Blandford-Znajek engine. In the weak-field and slow-rotation regime, P/M_H\ll1 and a/M_H\ll1, our general balance reproduces Wang's mass- and angular-momentum loss rates. The irreducible mass, M_{irr}=\sqrt{A_H/(16π)}, reveals what those rates do not show by themselves. It measures the part of the rotational work absorbed irreversibly by the horizon. At fixed magnetic flux and under impedance matching, half of the instantaneous rotational work leaves as electromagnetic power. The other half increases the horizon area and M_{irr}. The assumptions behind this reduction are derived explicitly. A minimal nondissipative world-volume action makes the current-sheet contribution vanish through O(p^2ε^2). Direct power counting of Wang's perturbative fields, together with a compatible canonical-flux prescription, gives a relative focusing and canonical correction of O(p^2)+O(ε^2). These estimates mark the range in which the reduced Blandford-Znajek trajectory remains controlled. Extending that trajectory to high spin requires an additional extrapolation. Relating the quasilocal horizon loss to energy measured at infinity requires a separate asymptotic flux calculation.
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