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arXiv 1306.4739gr-qcmath-phmath.DGmath.MP
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黑洞面积的质量、电荷和Angular Momentum下界

Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum

Sergio Dain, Marcus Khuri, Gilbert Weinstein, Sumio Yamada

摘要:

彭罗斯不等式的最一般的公式给出了黑洞的面积、电荷和角动量的ADM质量的下限。这个不等式又等价于剩余量的面积的上界和下界。本文在Einstein-麦克斯韦方程组的轴对称最大初始数据集下,当非电磁物质场不带电且满足主能量条件时,建立了单个黑洞的下界.证明了该不等式是饱和的当且仅当初始数据来自极端的Kerr-Newman时空。当电荷或角动量为零时,给出了进一步的改进。最后,我们讨论了在多个黑洞存在的情况下下界的有效性。

英文摘要:

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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