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Near-horizon metric : ウィキペディア英語版
Near-horizon metric
The near-horizon metric (NHM) refers to the near-horizon limit of the global metric of a black hole. NHMs play an important role in studying the geometry and topology of black holes, but are only well defined for extremal black holes.〔Hari K Kunduri, James Lucietti. ''A classification of near-horizon geometries of extremal vacuum black holes''. Journal of Mathematical Physics, 2009, 50(8): 082502. (arXiv:0806.2051v3 (hep-th) )〕〔Hari K Kunduri, James Lucietti. ''Static near-horizon geometries in five dimensions''. Classical and Quantum Gravity, 2009, 26(24): 245010. (arXiv:0907.0410v2 (hep-th) )〕〔Hari K Kunduri. ''Electrovacuum near-horizon geometries in four and five dimensions''. Classical and Quantum Gravity, 2011, 28(11): 114010. (arXiv:1104.5072v1 (hep-th) )〕 NHMs are expressed in Gaussian null coordinates, and one important property is that the dependence on the coordinate r is fixed in the near-horizon limit.
==NHM of extremal Reissner–Nordström black holes==

The metric of extremal Reissner–Nordström black hole is
:ds^2\,=\,-\Big(1-\frac\Big)^2\,dt^2+\Big(1-\frac\Big)^dr^2+r^2\,\big(d\theta^2+\sin^2\theta\,d\phi^2 \big)\,.
Taking the near-horizon limit
:t\mapsto \frac\,,\quad r\mapsto M+\epsilon\,\tilde\,,\quad \epsilon\to 0\,,
and then omitting the tildes, one obtains the near-horizon metric
:ds^2=-\frac\,dt^2+\frac\,dr^2+M^2\,\big(d\theta^2+\sin^2\theta\,d\phi^2 \big)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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