旋轉的黑洞可以是電磁電漿球體的來源。而這樣的系統可以用FFE去描述。但FFE是非線性的，一般只能用數值的方式解。在這篇碩論，我們考慮一個帶有磁場及角動量的黑洞，並注重在靠近視界上的區域。利用這區域的幾何對稱性去簡化FFE，並且得到解析解。

The rotating black hole can be the source of the plasma-filled of magnetosphere, which
can be describe by the FFE(Force Free Electromagnetic). The equation of the FFE is
highly nonlinear. In this thesis, we consider the extremal rotating charged black holes,
and calculute the FFE equations near the horizon where the energy emitted. We use
the symmetry of the near horizon extremal Kerr-Newman geometry to simplify the
equations, so that we can get the solutions of the FFE equations.

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