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萊斯納-諾德斯特洛姆度規 - Wikipedia

萊斯納-諾德斯特洛姆度規

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萊斯納-諾德斯特洛姆度規Reissner-Nordström metric)是广义相对论中描述描述静态球对称带电物体的引力场的度规,是广义相对论的一个著名的精確解,是雷斯勒(H.Reissner)以及诺斯特朗姆(G.Nordstrom)首先提出的。具有这样的度规形式的黑洞稱為萊斯納-諾德斯特洛姆黑洞

萊斯納-諾德斯特洛姆度規可以表示為:

\mathrm{d}s^2=-\mathrm{d}\tau^2=-\left(1-\frac{2GM}{r}+\frac{GQ^2}{4\pi r^2}\right)\mathrm{d}t^2 + \left(1-\frac{2GM}{r}+\frac{GQ^2}{4\pi r^2}\right)^{-1} \mathrm{d}r^2 +r^2 (\mathrm{d}\theta^2 +\sin^2\theta\,\mathrm{d}\phi^2)


廣義相對論
G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}\,
介紹
數學形式


電磁勢為

A_{\alpha} = \left(\frac{Q}{r}, 0, 0, 0\right)

可见电荷Q对度规的影响与r2成反比,是短程的,而引力质量的影响是长程的,因此一般情况下很少考虑电荷的作用。

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