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寮ㄥ绌剁娈点涓らユ绉涔甯歌锛绔㈢浠讳涓涓甫瀛瑰瀛涓璇介瑕娉ㄥ

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杩灏辨涓涓汉缁锛涓ョ涓绡跺跺ソ骞淬

Birkhoff瀹

骞夸稿璁洪㈡涓涓甯搁瑕缁锛灏辨Birkhoff瀹瀹涓锛寰澶骞夸稿璁虹璁＄芥Birkhoff瀹哄锛涓存姹瑙ｉ甯稿骞夸稿璁哄烘圭锛姣濡甯歌绾跨寮寮蹭灏辨搴璁＄

甯歌Birkhoff瀹琛ㄨ堪浠ュㄧㄤ娇ㄦ骞跨骞夸稿璁虹缁歌浣Gravitation㈡惧帮杩功ㄥ琚О涓衡澶ч涔ｇMTW锛涓哄㈡锛瀹规浜骞夸稿璁虹涔璁哄搴ㄤ功澶х害涓椤碉锛涓涓MisnerThorne锛靛奖绌胯绉瀛【储╋Wheeler箍涔稿璁虹绌剁澶ф濞

澶ч涔瀵Birkhoff瀹琛ㄨ堪濡涓

璇绉颁负Birkhoff瀹琛ㄨ堪锛浠讳瀵圭О绌哄哄浣芥タ浣

变㈢タ搴㈢M瀹涔涓哄寰r浠ュ昏川姝Birkhoff瀹甯稿父琚〃杩颁负锛浠讳瀵圭О绌哄哄浣涓澶ㄧ╄川褰卞辫寰浠ュ昏川冲

变涓〃杩板椤垮靛ㄤ达浣跨ㄨ捣ュ甯告逛究锛杩灏辨浜澶ч骞夸稿璁虹搴ㄧ虹锛姣濡㈣寮搴璁＄

藉板杩ラ娲锛

浣2009骞存褰剁瀛ㄩ拌绠╄川榛娲涓借涓搁跺涓㈢绉琛ㄨ堪璇锛澶ㄧ╄川锛灏辨界╄川锛涓浣褰卞ㄧ搴锛灏辨界╄川榛娲涔寸搴锛锛涓惰ㄧ存褰卞榛娲瑙ц川锛杩姝ｆㄨ娴藉扳瀹杩ラ娲

浠缁璁哄瀛锛ゥ捣榛绱㈡╃澶х浠涓村澶ㄨ娴涓解扳瀹杩ラ娲锛界板琚荤ㄨ澶涔灏辨璋荤锯锛朵

澶ч涔璇存锛澶ㄨ娴板娉㈣荤ㄩ娲瑙澶姘歌涓借锛浣ㄨ娴搴娉㈣繁杩浜

绱㈡╃璇存锛褰跺澶ч涔凤

杩浜澶х浠借涓哄敖绠″浼涓澶存榛娲锛浣㈢瑙娴扮存琚荤ㄩ娲瑙澶

涓轰瑙ｉ杩涓剧璋锛寰澶澶х杈╄В璇达跺娉㈣浜锛浣俊琚荤ㄤ瑙澶杩涓京瑙ｅ跺灏辨寮浜猴娌℃骞夸稿璁鸿绠虹锛

斤娉ㄦ涓涓炬í杞寸堕存宀搴娉㈠堕达涓よ涓界镐瀹ㄦ灏瀹涓搴娉㈣ラ娲瑙跺诲搴浜宀跨堕达涔灏辨ㄥ宀堕村锛搴娉㈡规借ラ娲锛涓扮涓扮锛杩浠朵澶х浠藉夸璁蹭锛

浠缁璁烘

浠板澶х浠缁璁哄ㄤ灏辨澶х浠拷ヤ瀹韩璐ㄩ瀹褰浜芥寮浣戒骇寮妫楠绮瀛浠璁＄瀹榛娲浣涓轰涓翠寮浣绯讳璧疯绠锛浠瀹璐ㄩ藉拷ョ锛杩浠璁＄澶х浠绠抽哄

褰舵浠娌℃冲跺板ｄ澶х浠ｆ峰骞Birkhoff瀹锛琛涓ユ肩璁＄锛ｄ骞挎瀵圭

灏界瀹璐ㄩ榛娲告璧锋ュ浠ュ拷ヤ璁★浣氨瑰垮井灏川涓斤灏辨榛娲浜ㄦ榛娲锛灏辨ラ姝ㄧ榛娲瑙浜ㄨ瑙锛灏卞ㄦ堕达瀹璁＄琛ㄦ涓堕村跺寰涓界╄川锛瀹锛濡榛娲锛榛娲瑙灏变浼ㄨ锛涓绠′界╄川璐ㄩ澶ч戒浼ㄥㄥ绯荤堕村杩ラ娲锛杩浠璁＄澶х浠绠川哄涔灏辨Birkhoff瀹涓芥骞垮版澶ㄧ╄川碉

濡浠缁璁哄ㄥ扳绌胯涓娉㈠伴娲版碉灏变寰板涓缁璁猴

锛1锛ㄩ娲澶㈢甯宀浠ョ板娉㈤『╄ラ娲锛涓荤ㄩ娲瑙澶

锛2锛ㄥㄥ宀堕村锛缇コ涔涓跨涓锛典搴娉㈢濂冲夸ㄥ扮涓绛稿ュ锛搴娉㈡娉拌揪榛娲涓锛姝ゆ娉寰版锛

锛3锛村涓ラ濡瀹瀹涓榛娲芥变╄川濉褰㈡锛璁哄瑙娴芥涓璁猴锛ｄㄥ瀹骞撮锛浠浠澶х害140浜垮勾锛锛榛娲涓濂光娌℃╄川锛褰惰涓濂光灏辨病版姝も绌胯靛奖绉瀛富棰灏辨浜锛

斤浠璁＄缁璁哄浜宀杩娉㈢堕达搴娉㈠ㄦ堕村灏辨ヤ榛娲锛褰惰ラ娲跺诲浜宀搴娉㈡姣濡涓や汉跺芥30宀锛搴娉㈣ョ跺甯宀宸茬50宀浜锛浣娉㈠村35宀锛蜂板榛娲璐ㄩ互涓や汉惰绂婚娲澶杩筹

澶х浠芥璇达

2012骞达锛澶涓涓浜涓绡绔锛璇璁ㄨ浜涓㈡璇寸甯哥ㄧBirkhoff瀹琛ㄨ堪璇浠涓Birkhoff瀹搴璇ユ病锛汉璇ㄤ

浠ュㄨ绡绔浠涓句11父ㄧ骞夸稿璁轰绉涔瑙㈢㈠Birkoff瀹璇〃杩帮娓╀集煎缁镐姣濡ㄤ缁歌浣╃瀹瀹瀛涓涓娈佃 The acceleration of the radius of the sphere is given by the Newtonian equation (D.24), because Birkhoffs theorem says the material outside the sphere cannot have any gravitational effect on the behavior of what is inside. 灏遍甯稿稿

锛Birkhoff汉璇达

浣舵杩颁澶锛浼拌寰澶浜轰涓锛姣绔涔骞夸稿璁轰绉涔芥瑰や涓涓绗骞介ｄ杞绘剧涓褰舵涔娌℃Birkhoff汉瀵硅涓璇浠琛ㄨ堪濮Birkhoff瀹琛ㄥㄤ汉1923骞村涓浣功藉澶х句功棣╃棣

涓宸х跺澶х╃绯诲ㄥ缓妤硷╃棣澶чㄥ涔借惧板颁瀹や锛娌℃烘ャ杩涓绛灏辨ソ骞达缁浜涓涔垮颁杩功锛澶版锛ㄦ瑰璋㈠澶уぉ绯诲浠版锛锛

璇ヤ功冲瀹圭浠濡涓

杩涔搴

剧涓绗4锛癸涔灏辨功缁璁猴灏辨璋Birkhoff瀹锛浠ㄨ琛ㄨ堪瀵圭О寮烘涓杩㈡璇寸浣跨ㄧ琛ㄨ堪烘淬

浣堕瑕浠板璇璇浠涔锛

Birkhoff瀹璇ㄨ涓绔澶冲衡

棣瀹涔浜澶冲衡锛寸绌洪存涓圭瀵圭О甯寮恒跺璇达浠虫敞涓╄川澶㈢寮恒

㈠璇璇达Birkhoff绌剁规氨娌℃澶ㄧ╄川锛姝ゆ璋澶ㄧ╄川涓藉奖ㄧ搴Birkhoff瀹姣崇郴锛瀹ㄦｄョ澶х浠互璁逛璁归锛

涓㈢Birkhoff汉ㄤ功涓蜂瀵笺

杩灏辨寰r澶搴涓浣タ搴涓扁r浠ュ璐ㄩm冲辨ャ浣r浠ュ涔娌℃╄川锛杩涓瑰汉藉璁颁锛

Birkhoff汉瑙ｉ

浠纭浜杩椤跨璁虹缁涓凤浣浠舵r浠ュ涔娌℃╄川锛杩涓瑰汉藉璁颁锛

浣涓藉ㄦ汉锛涓哄ㄧ椤跨璁洪㈢瀵圭О绯荤澶ㄧ╄川纭褰卞ㄧ寮猴㈢Birkhoff璇翠椤跨璁轰凤ｅ氨涓绠″ㄦ╄川浜锛戒峰э

Birkhoff汉荤

Birkhoff汉浠跺ㄥ己璋瀵圭О╄川澶ㄧ寮恒姝Birkhoff汉娌￠锛浣功涓涓版规病瑰娓Birkhoff瀹ㄨ达灏辫汉骞胯ㄤ

姝わ濮戒涪锛璇ヨ杩寰璇伙瀹ㄦ病灏辫锛杩寰澶э

Birkhoff, G. D. (1923). Relativity and Modern Physics. Cambridge, Massachusetts: Harvard University Press.

C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, W.H. Freeman, New York,1973.

P.J.E. Peebles, Principles of Physical Cosmology, Princeton: Princeton UniversityPress (1993), pp.63, pp.75

Liu, Yuan; Zhang, Shuang Nan, The exact solution for shells collapsing towards a pre-existing black hole,08/2009, Physics Letters B, Volume 679, Issue 2, p. 88-94

ZHANG, S.-N. & YI, S. On A Common Misunderstanding Of The Birkhoff Theorem And Light Deflection Calculation: Generalized Shapiro Delay And Its Possible Laboratory Test. International Journal of Modern Physics: Conference Series 12, 419430 (2012).

璇/骞Birkhoff瀹11箍涔稿璁烘绉涔涓

H.C. Ohanian, Gravitation and Spacetime, New York & London: W.W. NORTON & COMPANY (1976), pp. 301

M. Harwit, Astrophysical Concepts, Fourth Edition, New York: Springer Science+Business Media, LLC, (2006), pp.443, pp.573

S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, New York: Basic Books (1977), pp.37, pp.421

V. Mukhanov, Physical Foundations of Cosmology, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo: Cambridge University Press (2005), pp.9

J.A. Peacock, An Introduction to the Physics of Cosmology, in Modern Cosmology, S. Bonometto, V. Gorini & U Moschella (eds), Bristol & Philadelphia: Institute of Physics Publishing (2002), pp.22, pp.30

P. Coles, F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure,

Second Edition, West Sussex, England: John Wiley & Sons, Ltd, (2002), pp.24

C. Grupen, Astroparticle Physics, Berlin, Heidelberg, New York: Springer (2005),pp.178

R. Ferraro, Einsteins Space-Time: An Introduction to Special and General Relativity,New York: Springer Science+Business Media, LLC, (2007), pp.244

J.A. Peacock, Cosmological Physics, Cambridge: Cambridge University Press (1998),pp.58, pp.73

P.J.E. Peebles, Physical Cosmology, Princeton: Princeton University Press (1971),pp.11

P.J.E. Peebles, Principles of Physical Cosmology, Princeton: Princeton UniversityPress (1993), pp.63, pp.75

娉

娉1锛ㄦユ跺锛2005骞存浜烘版猴跺Birkhoff瀹绗娆″虹ㄦ㈡╀Birkhoff 1923骞寸ｆ功锛涓澶浜Jebsen浜1921骞村琛ㄧ锛璇璇疯WikiBirkhoff's Theorem＄浠ョュ璇ュBirkhoff-Jebsen瀹村涓杩杩杩璁ㄨ涓婚炽

娉2锛杩ㄥ浜澶у灏辫涓浣浜涓や釜ュ锛绗娆℃ㄧ邯蹇靛箍涔稿璁100ㄥ勾浼璁浼浣浜猴瀛A锛璇锛浜猴瀛B锛娌℃浼璁浜ュ涔璇浠锛瀛A锛锛浠锛瀛B锛浠ュ绌惰Birkhoff瀹锛璇Birkhoff瀹浠ョㄥㄥㄦ╄川点澶翠炬轰瀛B浜ゆ涓涓

寮

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