[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/106869#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/106869","headline":"\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f – Wikipedia","name":"\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f – Wikipedia","description":"\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f\uff08\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u307b\u3046\u3066\u3044\u3057\u304d\u3001\u82f1\u8a9e: Tolman\u2013Oppenheimer\u2013Volkoff equation\uff09\u306f\u5b87\u5b99\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u3001\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u3067\u306e\u9759\u7684\u91cd\u529b\u5e73\u8861\u306b\u3042\u308b\u7b49\u65b9\u306a\u7403\u5bfe\u79f0\u306a\u7269\u8cea\u306e\u69cb\u9020\u3092\u6c7a\u5b9a\u3059\u308b\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u3002\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u3067\u3042\u308b[1]\u3002 dP(r)dr=\u2212Gr2[\u03c1(r)+P(r)c2][M(r)+4\u03c0r3P(r)c2][1\u22122GM(r)c2r]\u22121\u00a0.{displaystyle {frac {dP(r)}{dr}}=-{frac {G}{r^{2}}}left[rho (r)+{frac {P(r)}{c^{2}}}right]left[M(r)+4pi r^{3}{frac {P(r)}{c^{2}}}right]left[1-{frac {2GM(r)}{c^{2}r}}right]^{-1} .} \u3053\u3053\u3067r\u306f\u7403\u9762\u5ea7\u6a19\u3067\u306e\u5909\u6570\u3067\u3042\u308b\u3002\u305d\u3057\u3066\u3001\u03c1(r0) \u3068 P(r0)\u306f\u305d\u308c\u305e\u308cr=r0\u306e\u4f4d\u7f6e\u306e\u5bc6\u5ea6\u3068\u5727\u529b\u3067\u3042\u308b\u3002M(r0)\u306f\u8ddd\u96e2\u304c\u96e2\u308c\u305f\u89b3\u6e2c\u8005\u304c\u91cd\u529b\u5834\u304b\u3089\u611f\u3058\u308b\u534a\u5f84r=r0\u306e\u4e2d\u306b\u3042\u308b\u5408\u8a08\u8cea\u91cf\u3067\u3042\u308b\u3002\u305d\u308c\u306fM(0)=0 \u3068\u6b21\u306e\u5f0f\u3092\u6e80\u305f\u3059[1]\u3002 dM(r)dr=4\u03c0\u03c1(r)r2\u00a0.{displaystyle {frac {dM(r)}{dr}}=4pi","datePublished":"2022-03-23","dateModified":"2022-03-23","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f1022de7243247714bfeabd9adb6a74c5a0de48f","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f1022de7243247714bfeabd9adb6a74c5a0de48f","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/106869","about":["Wiki"],"wordCount":3163,"articleBody":"\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f\uff08\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u307b\u3046\u3066\u3044\u3057\u304d\u3001\u82f1\u8a9e: Tolman\u2013Oppenheimer\u2013Volkoff equation\uff09\u306f\u5b87\u5b99\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u3001\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u3067\u306e\u9759\u7684\u91cd\u529b\u5e73\u8861\u306b\u3042\u308b\u7b49\u65b9\u306a\u7403\u5bfe\u79f0\u306a\u7269\u8cea\u306e\u69cb\u9020\u3092\u6c7a\u5b9a\u3059\u308b\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u3002\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u3067\u3042\u308b[1]\u3002dP(r)dr=\u2212Gr2[\u03c1(r)+P(r)c2][M(r)+4\u03c0r3P(r)c2][1\u22122GM(r)c2r]\u22121\u00a0.{displaystyle {frac {dP(r)}{dr}}=-{frac {G}{r^{2}}}left[rho (r)+{frac {P(r)}{c^{2}}}right]left[M(r)+4pi r^{3}{frac {P(r)}{c^{2}}}right]left[1-{frac {2GM(r)}{c^{2}r}}right]^{-1} .}  \u3053\u3053\u3067r\u306f\u7403\u9762\u5ea7\u6a19\u3067\u306e\u5909\u6570\u3067\u3042\u308b\u3002\u305d\u3057\u3066\u3001\u03c1(r0) \u3068 P(r0)\u306f\u305d\u308c\u305e\u308cr=r0\u306e\u4f4d\u7f6e\u306e\u5bc6\u5ea6\u3068\u5727\u529b\u3067\u3042\u308b\u3002M(r0)\u306f\u8ddd\u96e2\u304c\u96e2\u308c\u305f\u89b3\u6e2c\u8005\u304c\u91cd\u529b\u5834\u304b\u3089\u611f\u3058\u308b\u534a\u5f84r=r0\u306e\u4e2d\u306b\u3042\u308b\u5408\u8a08\u8cea\u91cf\u3067\u3042\u308b\u3002\u305d\u308c\u306fM(0)=0 \u3068\u6b21\u306e\u5f0f\u3092\u6e80\u305f\u3059[1]\u3002  dM(r)dr=4\u03c0\u03c1(r)r2\u00a0.{displaystyle {frac {dM(r)}{dr}}=4pi rho (r)r^{2} .}\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u4e00\u822c\u7684\u306b\u6642\u9593\u4e0d\u5909\u3067\u7403\u5bfe\u79f0\u306a\u8a08\u91cf\u306e\u3082\u3068\u3067\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u3067\u5c0e\u304b\u308c\u308b\u3002\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u3064\u3044\u3066\u3001\u3053\u306e\u8a08\u91cf\u306f\u6b21\u306e\u5f62\u3092\u3068\u308b[1]\u3002ds2=e\u03bd(r)c2dt2\u2212(1\u22122GM(r)\/rc2)\u22121dr2\u2212r2(d\u03b82+sin2\u03b8d\u03d52)\u00a0,{displaystyle ds^{2}=e^{nu (r)}c^{2}dt^{2}-(1-2GM(r)\/rc^{2})^{-1}dr^{2}-r^{2}(dtheta ^{2}+mathrm {sin} ^{2}theta dphi ^{2}) ,}\u3053\u3053\u3067\u03bd(r)\u306f\u6761\u4ef6\u306b\u3088\u308a\u6c7a\u5b9a\u3055\u308c\u308b\u5b9a\u6570[1]\u3067\u3042\u308b\u3002  d\u03bd(r)dr=\u22122P(r)+\u03c1(r)c2dP(r)dr.{displaystyle {frac {dnu (r)}{dr}}=-{frac {2}{P(r)+rho (r)c^{2}}}{frac {dP(r)}{dr}}.}\u72b6\u614b\u65b9\u7a0b\u5f0f F(\u03c1, P)=0 \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u5bc6\u5ea6\u3068\u5727\u529b\u3092\u95a2\u4fc2\u4ed8\u3051\u3001\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f\u306f\u5e73\u8861\u306b\u3042\u308b\u7b49\u65b9\u306a\u7403\u5bfe\u79f0\u306a\u7269\u8cea\u306e\u69cb\u9020\u3092\u5b8c\u5168\u306b\u6c7a\u5b9a\u3059\u308b\u3002\u3082\u30571\/c2\u306e\u5927\u304d\u3055\u306e\u9805\u3092\u7121\u8996\u3059\u308b\u3068\u304d\u3001\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u9759\u6c34\u5727\u65b9\u7a0b\u5f0f(hydrostatic equation)\u3068\u306a\u308a\u3001\u5e73\u8861\u306b\u3042\u308b\u7b49\u65b9\u306a\u7403\u5bfe\u79f0\u306a\u7269\u8cea\u3067\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u88dc\u6b63\u304c\u91cd\u8981\u3067\u306a\u3044\u3068\u304d\u306b\u7528\u3044\u3089\u308c\u308b\u3002\u3082\u3057\u771f\u7a7a\u4e2d\u306e\u7403\u9762\u5883\u754c\u3067\u3042\u308b\u7269\u8cea\u306e\u6a21\u578b\u3067\u65b9\u7a0b\u5f0f\u304c\u4f7f\u308f\u308c\u308b\u3068\u304d\u3001\u5727\u529b\u304c\u7121\u3044\u6761\u4ef6P(r)=0\u3068e\u03bd(r)=1\uff0d2GM(r)\/rc2\u304c\u5883\u754c\u6761\u4ef6\u3068\u3057\u3066\u8ab2\u3055\u308c\u308b\u3002\u4e8c\u756a\u76ee\u306e\u5883\u754c\u6761\u4ef6\u306f\u771f\u7a7a\u306e\u9759\u7684\u7403\u5bfe\u79f0\u5834\u306e\u65b9\u7a0b\u5f0f\u89e3\u306f\u4e00\u610f\u306b\u6b21\u306e\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u8a08\u91cf\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u8ab2\u3055\u308c\u308b\u3002ds2=(1\u22122GM0\/rc2)c2dt2\u2212(1\u22122GM0\/rc2)\u22121dr2\u2212r2(d\u03b82+sin2\u03b8d\u03d52)\u00a0.{displaystyle ds^{2}=(1-2GM_{0}\/rc^{2})c^{2}dt^{2}-(1-2GM_{0}\/rc^{2})^{-1}dr^{2}-r^{2}(dtheta ^{2}+mathrm {sin} ^{2}theta dphi ^{2}) .}\u3053\u3053\u3067M0\u306f\u3082\u3046\u4e00\u5ea6\u8aac\u660e\u3059\u308b\u3068\u9060\u304f\u306b\u96e2\u308c\u305f\u89b3\u6e2c\u8005\u304c\u91cd\u529b\u5834\u304b\u3089\u611f\u3058\u308b\u8cea\u91cf\u306e\u5408\u8a08\u3067\u3042\u308b\u3002\u5883\u754c\u3092r=rB\u3068\u3059\u308b\u3068\u3001M(r)\u306e\u5b9a\u7fa9\u306f\u6b21\u306e\u5f0f\u3092\u8981\u6c42\u3059\u308b\u3002M0=M(rB)=\u222b0rB4\u03c0\u03c1(r)r2dr\u00a0.{displaystyle M_{0}=M(r_{B})=int _{0}^{r_{B}}4pi rho (r)r^{2},dr .}\u7269\u4f53\u306e\u5bc6\u5ea6\u3092\u4f53\u7a4d\u306b\u3064\u3044\u3066\u7a4d\u5206\u3057\u3066\u8a08\u7b97\u3059\u308b\u3002\u3053\u308c\u306b\u5bfe\u3057\u3066\u3001\u6b21\u306e\u91cf\u3092\u8003\u3048\u308b\u3002M1=\u222b0rB4\u03c0\u03c1(r)r21\u22122GM(r)\/rc2\u00a0,dr.{displaystyle M_{1}=int _{0}^{r_{B}}{frac {4pi rho (r)r^{2}}{sqrt {1-2GM(r)\/rc^{2}}}} ,dr.}\u3053\u306e\u4e8c\u3064\u306e\u91cf\u306e\u5dee\u306f\u03b4M=\u222b0rB4\u03c0\u03c1(r)r2((1\u22122GM(r)\/rc2)\u22121\/2\u22121)dr,{displaystyle delta M=int _{0}^{r_{B}}4pi rho (r)r^{2}((1-2GM(r)\/rc^{2})^{-1\/2}-1),dr,}\u3053\u306e\u5dee\u306f\u91cd\u529b\u306e\u675f\u7e1b\u30a8\u30cd\u30eb\u30ae\u30fc\u3092c2\u3067\u5272\u3063\u305f\u3082\u306e\u3068\u306a\u308b\u3002  \u4e2d\u6027\u5b50\u661f\u306e\u72b6\u614b\u65b9\u7a0b\u5f0f\u304b\u3089\u8cea\u91cf\u3068\u534a\u5f84\u306e\u95a2\u4fc2\u3092\u8868\u3057\u305f\u56f3\u3002\u4e00\u3064\u306fK\u4e2d\u9593\u5b50\u306e\u7e2e\u9000\u3092\u542b\u3080\u5834\u5408\uff08\u7dd1\u7dda\uff09\u3067 \u3001\u4ed6\u65b9\u306fK\u4e2d\u9593\u5b50\u306e\u7e2e\u9000\u304c\u7121\u3044\u5834\u5408\uff08\u8d64\u7dda\uff09\u3067\u3042\u308b \u3002\u70b9\u306f\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u9650\u754c\u3001\u8a00\u3044\u63db\u3048\u308b\u3068 \u56de\u8ee2\u3092\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u3067\u306e\u6700\u5927\u8cea\u91cf\u306b\u5bfe\u5fdc\u3059\u308b\u3002 \u72b6\u614b\u65b9\u7a0b\u5f0f\u306f: \u7dd1\u7dda: N.K. Glendenning and J. Schaffner-Bielich, Phys. Rev. C 60, 025803 (1999), \u8d64\u7dda: J. Zimanyi and S.A. Moszkowski, Phys. Rev. C 42, 1416 (1990)\u3092\u7528\u3044\u305f\u3002\u30c8\u30eb\u30de\u30f3\u306f1934\u5e74\u30681939\u5e74\u306b\u7403\u5bfe\u79f0\u306a\u8a08\u91cf\u3092\u89e3\u6790\u3057\u305f[2][3]\u3002\u65b9\u7a0b\u5f0f\u306e\u5f62\u306f1939\u5e74\u306b\u30ed\u30d0\u30fc\u30c8\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u3068\u30f4\u30a9\u30eb\u30b3\u30d5\u306b\u3088\u308a”On Massive Neutron Cores”[1]\u306e\u8ad6\u6587\u3067\u5c0e\u304b\u308c\u305f\u3002\u3053\u306e\u8ad6\u6587\u3067\u306f\u4e2d\u6027\u5b50\u306e\u7e2e\u9000\u3057\u305f\u30d5\u30a7\u30eb\u30df\u30ac\u30b9\u306e\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066\u3001\u4e2d\u6027\u5b50\u661f\u306e\u91cd\u529b\u8cea\u91cf\u4e0a\u9650\u304c\u304a\u3088\u305d0.7\u592a\u967d\u8cea\u91cf\u3067\u3042\u308b\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002\u3053\u306e\u72b6\u614b\u65b9\u7a0b\u5f0f\u306f\u73fe\u5b9f\u7684\u306a\u4e2d\u6027\u5b50\u661f\u306e\u3082\u306e\u3067\u306f\u306a\u3044\u3053\u3068\u304b\u3089\u4e0d\u6b63\u78ba\u3067\u3042\u308b\u3002\u73fe\u4ee3\u306e\u63a8\u5b9a\u3067\u306f\u9650\u754c\u306e\u7bc4\u56f2\u306f1.5\u304b\u30893.0\u592a\u967d\u8cea\u91cf\u3067\u3042\u308b[4]\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]^ a b c d e On Massive Neutron Cores, J. R. Oppenheimer and G. M. Volkoff, Physical Review 55, #374 (February 15, 1939), pp. 374\u2013381.^ Effect of Inhomogeneity on Cosmological Models, Richard C. Tolman, Proceedings of the National Academy of Sciences 20, #3 (March 15, 1934), pp. 169\u2013176.^ Static Solutions of Einstein’s Field Equations for Spheres of Fluid, Richard C. Tolman, Physical Review 55, #374 (February 15, 1939), pp. 364\u2013373.^ The maximum mass of a neutron star, I. Bombaci, Astronomy and Astrophysics 305 (January 1996), pp. 871\u2013877.\u95a2\u9023\u8a18\u4e8b[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki22\/archives\/106869#breadcrumbitem","name":"\u30c8\u30eb\u30de\u30f3\u30fb\u30aa\u30c3\u30da\u30f3\u30cf\u30a4\u30de\u30fc\u30fb\u30f4\u30a9\u30eb\u30b3\u30d5\u65b9\u7a0b\u5f0f – Wikipedia"}}]}]