{"id":32076,"date":"2024-02-20T23:52:10","date_gmt":"2024-02-20T23:52:10","guid":{"rendered":"https:\/\/science-hub.click\/%E3%82%AF%E3%83%A9%E3%82%B9%E3%82%AB%E3%83%AB%E3%83%BB%E3%82%BB%E3%83%BC%E3%82%B1%E3%83%AC%E3%82%B9%E6%8C%87%E6%A8%99-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-02-20T23:52:10","modified_gmt":"2024-02-20T23:52:10","slug":"%E3%82%AF%E3%83%A9%E3%82%B9%E3%82%AB%E3%83%AB%E3%83%BB%E3%82%BB%E3%83%BC%E3%82%B1%E3%83%AC%E3%82%B9%E6%8C%87%E6%A8%99-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=32076","title":{"rendered":"\u30af\u30e9\u30b9\u30ab\u30eb\u30fb\u30bb\u30fc\u30b1\u30ec\u30b9\u6307\u6a19 – \u5b9a\u7fa9"},"content":{"rendered":"

Kruskal-Szeres \u30e1\u30c8\u30ea\u30af\u30b9\u306f\u3001<\/strong> Schwarzschild \u30e1\u30c8\u30ea\u30af\u30b9\u3092\u6700\u5927\u9650\u306b\u5206\u6790\u7684\u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u30af\u30e9\u30b9\u30ab\u30eb\u30fb\u30bb\u30fc\u30b1\u30ec\u30b9\u8a08\u91cf\u306e\u5c0e\u5165\u306f\u3001\u30b7\u30e5\u30ef\u30eb\u30c4\u30b7\u30eb\u30c8\u306e\u8a08\u91cf\u306b\u5bfe\u3059\u308b\u8ffd\u52a0\u306e\u89e3\u6c7a\u7b56\u3092\u63d0\u4f9b\u3057\u3001\u7279\u306b\u30d6\u30e9\u30c3\u30af \u30db\u30fc\u30eb\u3001\u3064\u307e\u308a\u30db\u30ef\u30a4\u30c8<\/a><\/span>\u30db\u30fc\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u30c9\u30e1\u30a4\u30f3\u3068\u4e8c\u91cd\u306e\u30c9\u30e1\u30a4\u30f3\u3092\u767a\u898b\u3057\u307e\u3059\u3002<\/p>

1960 \u5e74\u3001\u30af\u30e9\u30b9\u30ab\u30eb\u3068\u30bb\u30fc\u30b1\u30ec\u30b9\u306f\u3001\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u534a\u5f84<\/a><\/span>\u306b\u5b58\u5728\u3059\u308b\u91cd\u529b\u7279\u7570\u70b9\u304c<\/a><\/span>\u771f\u306e\u7269\u7406\u7684<\/a><\/span>\u7279\u7570\u70b9\u3067\u306f\u306a\u3044\u3053\u3068\u3092\u767a\u898b\u3057\u307e\u3057\u305f\u3002\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6<\/a><\/span>\u3067\u306f\u3001\u89b3\u5bdf\u53ef\u80fd\u306a\u52b9\u679c\u306f\u30ea\u30fc\u30de\u30f3 \u30c6\u30f3\u30bd\u30eb<\/a><\/span>\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u8a08\u91cf<\/a><\/span>\u306b\u5b58\u5728\u3059\u308b\u7279\u7570\u70b9\u306f\u3001\u81ea\u7531\u843d\u4e0b\u3067\u89b3\u6e2c\u8005\u304c\u7d4c\u9a13\u3059\u308b\u6f6e\u6c50<\/a><\/span>\u529b\u3068\u3001\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u534a\u5f84\u306e<\/a><\/span>\u30ec\u30d9\u30eb<\/i>\u3067<\/i>\u7121\u9650\u5927\u3068<\/i>\u306a\u308b<\/i><\/sup>R<\/i> a<\/i> b<\/i> c<\/i> d<\/i>\u304c<\/i><\/sub><\/span>\u9069\u5207\u306a\u5ea7\u6a19\u3092<\/a><\/span>\u57fa\u6e96\u306b\u3057\u3066\u8868\u73fe\u3055\u308c\u308b\u3068\u305d\u3046\u3067\u306f\u306a\u3044\u3088\u3046\u306a\u66f2\u7387<\/a><\/span>\u4e0d\u5909\u91cf\u306b\u95a2\u4fc2\u3057\u307e\u3059\u3002\u30b7\u30b9\u30c6\u30e0<\/a><\/span>\u3002\u5730\u7403<\/a><\/span>\u4e0a\u306e\u5317\u6975<\/a><\/span>\u306e\u3088\u3046\u306b\u3001\u3053\u308c\u306f\u5358\u7d14\u306a\u70b9<\/a><\/span>\u3067\u3059\u304c\u3001\u7279\u5b9a\u306e\u5ea7\u6a19\u7cfb\u3067\u306f\u7279\u7570\u70b9\u306b\u306a\u308a\u3001\u305f\u3068\u3048\u3070\u8d64\u9053\u6295\u5f71<\/a><\/span>\u306e\u3088\u3046\u306b\u76f4\u7dda\u4e0a\u306b\u5e83\u304c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u6975\u6295\u5f71\u3067\u306f\u5b8c\u5168\u306b<\/a><\/span>\u901a\u5e38\u306e\u65b9\u6cd5\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u7279\u7570\u70b9\u306f\u3001\u5ea7\u6a19\u7279\u7570\u70b9<\/i>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

Schwarzschild \u8a08\u91cf\u304b\u3089 Kruskal-Szeres \u8a08\u91cf\u306b\u79fb\u52d5\u3059\u308b<\/a><\/span>\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u5ea7\u6a19\u5909\u66f4\u306e\u91cd\u8981\u306a\u30b9\u30c6\u30c3\u30d7\u306f\u3001Regge-Wheeler\u30bf\u30fc\u30c8\u30eb<\/i>\u5ea7\u6a19r<\/i> *<\/sub><\/span>\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002 <\/p>

$$ {r_* = r + r_S \\ln\\left({r \\over r_S} -1\\right)} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 r<\/i> S \u306f<\/i><\/sub><\/span>\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u534a\u5f84\u3067\u3059

$$ {\\frac{2GM}{c^2}} $$<\/div>\u305d\u3057\u3066\u305d\u308c\u306fr<\/i> S<\/i><\/sub><\/span>\u3067\u9023\u7d9a\u3057\u305f\u307e\u307e\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

\u3053\u308c\u304b\u3089\u30012 \u3064\u306e\u65b0\u3057\u3044\u5ea7\u6a19\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {u = ct + r_* \\;} $$<\/div><\/dd>
$$ {v = ct – r_* \\;} $$<\/div><\/dd><\/dl>

\u3053\u308c\u3089\u306e\u5ea7\u6a19\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30b7\u30e5\u30f4\u30a1\u30eb\u30c4\u30b7\u30eb\u30c8\u6307\u6a19\u306ert<\/i>\u90e8\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {d\\,s^2 = – \\left(1 – \\frac{r_S}{r}\\right)\\,du\\,dv} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 r<\/i><\/span>\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308bu<\/i><\/span>\u3068v<\/i><\/span>\u306e\u95a2\u6570\u3068\u307f\u306a\u3055\u308c\u307e\u3059\u3002 <\/p>

$$ {r + r_S \\ln\\left({r \\over r_S} -1\\right) = r_* = (u -v)\/2} $$<\/div><\/dd><\/dl>

\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u5ea7\u6a19( u<\/i> , r<\/i> )<\/span>\u307e\u305f\u306f( v<\/i> , r<\/i> )<\/span>\u306f\u3001\u30a8\u30c7\u30a3\u30f3\u30c8\u30f3-\u30d5\u30a3\u30f3\u30b1\u30eb\u30b7\u30e5\u30bf\u30a4\u30f3\u5ea7\u6a19<\/i>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

\u305d\u306e\u5f8c\u3001\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {ds^2 = – \\frac{r_S e^{-r\/r_S}}{r} e^{{v-u}\/{2r_S}}\\,du\\,dv} $$<\/div><\/dd><\/dl>

\u65b0\u3057\u3044\u9023\u7d61\u5148\u306e\u8a73\u7d30\u3092\u5165\u529b\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {U = -e^{-u\/2r_S}} $$<\/div><\/dd>
$$ {V = e^{v\/2r_S}} $$<\/div><\/dd><\/dl>

\u30e1\u30c8\u30ea\u30af\u30b9\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {ds^2 = \\frac{4r_S^3 e^{-r\/r_S}}{r}\\,dU\\,dV} $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066r<\/i> = r<\/i> S\u3001<\/i><\/sub><\/span>\u3064\u307e\u308aU<\/i> = 0<\/span>\u307e\u305f\u306fV<\/i> = 0<\/span>\u3067\u306f\u7279\u7570\u70b9\u306f\u306a\u304f\u306a\u308a\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u30b7\u30e5\u30ef\u30eb\u30c4\u30b7\u30eb\u30c8\u306e\u89e3\u306f\u3001 r<\/i> > 0<\/span>\u3067\u3042\u308b\u3059\u3079\u3066\u306e\u5024\u306b\u62e1\u5f35\u3055\u308c\u307e\u3057\u305f\u3002 R<\/i> a<\/i> b<\/i> c<\/i> d<\/i><\/sub> R<\/i> a<\/i> b<\/i> c<\/i> d<\/i><\/sup>\u3092<\/span>\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u78ba\u8a8d\u3067\u304d\u308b\u3088\u3046\u306b\u3001 r<\/i> = 0<\/span>\u306b\u5b58\u5728\u3059\u308b\u7279\u7570\u70b9\u306f\u6301\u7d9a\u3057\u307e\u3059\u3002\u305d\u308c\u306f\u7269\u7406\u7684\u306a\u7279\u7570\u70b9\u3067\u3059\u3002<\/p>

Kruskal \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u305f<\/span>\u5f62\u5f0f\u306b\u306f\u3001\u6700\u7d42\u7684\u306a\u5ea7\u6a19\u5909\u63db\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>

T<\/i> = ( V<\/i> + U<\/i> ) \/ 2<\/span><\/dd>
X<\/i> = ( V<\/i> \u2212 U<\/i> ) \/ 2<\/span><\/dd><\/dl>

\u89d2\u306e\u90e8\u5206\u3092\u518d\u5c0e\u5165\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {ds^2 = \\frac{4r_S^3 e^{-r\/r_S}}{r}\\,(dX^2 – dT^2) + r^2(d\\theta^2 + \\sin^2\\theta\\,d\\phi^2)} $$<\/div><\/dd><\/dl>

\u5909\u6570T<\/i><\/span>\u304a\u3088\u3073X<\/i><\/span>\u306e\u5b9a\u7fa9\u57df\u306f\u3001\u6761\u4ef6r<\/i> > 0<\/span>\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059:<\/p>

X<\/i> 2<\/sup> \u2212 T<\/i> 2<\/sup> > \u2212 1<\/span><\/dd><\/dl><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u0645\u062a\u0631\u064a (\u062a\u0648\u0636\u064a\u062d) \u2013 arabe<\/a><\/li>
  2. Metrik \u2013 bavarois<\/a><\/li>
  3. Metrika \u2013 tch\u00e8que<\/a><\/li>
  4. Metrik \u2013 danois<\/a><\/li>
  5. Metrik \u2013 allemand<\/a><\/li>
  6. \u039c\u03b5\u03c4\u03c1\u03b9\u03ba\u03ae \u2013 grec<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u30af\u30e9\u30b9\u30ab\u30eb\u30fb\u30bb\u30fc\u30b1\u30ec\u30b9\u6307\u6a19 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n