{"id":3390,"date":"2022-08-19T00:00:12","date_gmt":"2022-08-18T15:00:12","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=3390"},"modified":"2022-08-25T10:01:11","modified_gmt":"2022-08-25T01:01:11","slug":"%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%82%92%e9%81%8b%e5%8b%95%e3%81%99%e3%82%8b%e8%a6%b3%e6%b8%ac%e8%80%85%e3%81%ab%e3%82%88%e3%82%8b%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e8%b5%a4%e6%96%b9%e5%81%8f%e7%a7%bb%e3%81%ae%e7%b5%b1%e4%b8%80%e7%9a%84%e7%90%86%e8%a7%a3\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%82%92%e9%81%8b%e5%8b%95%e3%81%99%e3%82%8b%e8%a6%b3%e6%b8%ac%e8%80%85%e3%81%ab%e3%82%88%e3%82%8b%e5%85%89%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc\/","title":{"rendered":"\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306b\u3088\u308b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c"},"content":{"rendered":"

\u4e16\u306e\u4e2d\u306e\u6559\u79d1\u66f8\u306b\u3088\u308b\u6a19\u6e96\u7684\u306a\u8aac\u660e\u3067\u306f\uff0c\u5149\u6e90\u3042\u308b\u3044\u306f\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u306b\u3088\u308b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\uff0c\u91cd\u529b\u304c\u306a\u3044\u5834\u5408\u306e\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u3067\u306e\u307f\u6709\u52b9\u3067\u3042\u308b\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u7528\u3044\u3066\u8aac\u660e\u3055\u308c\u3066\u3044\u305f\u3002\u91cd\u529b\u304c\u3042\u308b\u5834\u5408\u306f\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u305f\u3081\uff0c\u5225\u9014\u7406\u5c48\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u4e00\u65b9\u3067\uff0c\u91cd\u529b\u8d64\u65b9\u504f\u79fb\u306e\u6a19\u6e96\u7684\u306a\u8aac\u660e\u306f\uff0c\u91cd\u529b\u5834\u4e2d\u306b\u304a\u3044\u3066\u5149\u6e90\u3082\u89b3\u6e2c\u8005\u3082\u9759\u6b62\u3057\u3066\u3044\u308b\u5834\u5408\u306b\u306e\u307f\u6709\u52b9\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u3067\u306f\uff0c\u91cd\u529b\u5834\u4e2d\u3092\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e\u89b3\u6e2c\u3059\u308b\u5149\u306e\u632f\u52d5\u6570\uff08\u3084\u6ce2\u9577\uff09\u3092\u8abf\u3079\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>\n

\u3053\u3053\u3067\u306f\uff0c\u8d64\u65b9\u504f\u79fb\u3092\u7d71\u4e00\u7684\u306b\u7406\u89e3\u3059\u308b\u65b9\u6cd5\u306b\u5f93\u3063\u3066\uff0c<\/p>\n

I. \u91cd\u529b\u5834\u4e2d\u306e\u5149\u306e\u4f1d\u64ad\u306f\uff0c\u30cc\u30eb\u6e2c\u5730\u7dda\u3067\u4e0e\u3048\u3089\u308c\u308b<\/p>\n

II. 4\u5143\u901f\u5ea6 $u^{\\mu}$ \u306e\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u5149\u306e\u632f\u52d5\u6570\u306f $\\omega = – k_{\\mu} u^{\\mu}$ \u3067\u4e0e\u3048\u3089\u308c\u308b<\/p>\n

\u3068\u3044\u30462\u3064\u306e\u539f\u7406\u539f\u5247\u304b\u3089\uff0c\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u3092\u5c0e\u304f\u3002<\/p>\n

<\/h3>\n

\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u4f1d\u64ad\u3059\u308b\u5149<\/h3>\n

\u5149\u306e4\u5143\u6ce2\u6570\u30d9\u30af\u30c8\u30eb\u3092 $k^{\\mu}$ \u3068\u3059\u308b\u3068\uff0c\u52d5\u5f84\u65b9\u5411\u306b\u4f1d\u64ad\u3059\u308b\u3053\u3068\u304b\u3089<\/p>\n

$$k^{\\mu} = (k^0, k^1, 0, 0)$$<\/p>\n

\u6e2c\u5730\u7dda\u65b9\u7a0b\u5f0f\u306f\u5225\u30da\u30fc\u30b8\u300c\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u306e\u5149\u306e\u4f1d\u64ad<\/a>\u300d\u3067\u89e3\u3044\u3066\u3044\u308b\u304b\u3089\uff0c\u305d\u306e\u7d50\u679c\u3092\u4f7f\u3046\u3068\uff0c$k_{\\mu} = g_{\\mu\\nu} \\,k^{\\nu}$ \u306b\u3064\u3044\u3066<\/p>\n

$$k_{\\mu} = \\left(k_0, k_1, 0, 0 \\right) = \\left(-\\omega_c, \\ \\pm \\frac{\\omega_c}{1 – \\frac{r_g}{r}}, \\ 0, \\ 0 \\right)$$
\n\u8907\u53f7 \\(\\pm\\) \u306f\uff0c\u52d5\u5f84\u65b9\u5411\u5916\u5411\u304d\u306b\u4f1d\u64ad\u3059\u308b\u5149\u306b\u5bfe\u3057\u3066\u30d7\u30e9\u30b9\uff0c\u5185\u5411\u304d\u306e\u5149\u306b\u5bfe\u3057\u3066\u30de\u30a4\u30ca\u30b9\u3092\u3068\u308b\u3002<\/p>\n

 <\/p>\n

\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u306e\u9759\u6b62\u89b3\u6e2c\u8005<\/h3>\n

\u9759\u6b62\u89b3\u6e2c\u8005\u306e4\u5143\u901f\u5ea6 $u^{\\mu}$ \u306f<\/p>\n

$$u^{\\mu} = \\left(u^0, 0, 0, 0\\right) = \\left(\\frac{1}{\\sqrt{1 – \\frac{r_g}{r}}}, 0, 0, 0\\right)$$<\/p>\n

\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u5149\u306e\u632f\u52d5\u6570\u306f<\/p>\n

$$\\omega = – k_{\\mu} u^{\\mu} = – k_{0} u^{0} = \\frac{\\omega_c}{\\sqrt{1 – \\frac{r_g}{r}}}$$<\/p>\n

$r = r_1$ \u306e\u5149\u6e90\u304b\u3089\u632f\u52d5\u6570 $\\omega_1$ \u3067\u653e\u51fa\u3055\u308c\u305f\u5149\u3092\uff0c\u96e2\u308c\u305f\u4f4d\u7f6e $r\\ (> r_1)$ \u3067\u89b3\u6e2c\u3057\u305f\u6642\u306e\u632f\u52d5\u6570\u3092 $\\omega$ \u3068\u3059\u308b\u3068\uff0c<\/p>\n

$$\\frac{\\omega}{\\omega_1} = \\frac{\\sqrt{1 – \\frac{r_g}{r_1}}}{\\sqrt{1 – \\frac{r_g}{r}}} < 1 \\quad (r_g < r_1 < r)$$<\/p>\n

\u3053\u308c\u304c\uff0c\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u91cd\u529b\u8d64\u65b9\u504f\u79fb<\/a>\u3002<\/p>\n

\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005<\/h3>\n

\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e4\u5143\u901f\u5ea6 $\\bar{u}^{\\mu}$ \u306f\uff0c\u5225\u30da\u30fc\u30b8\u300c\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005<\/a>\u300d\u3067\u8a08\u7b97\u3057\u305f\u3088\u3046\u306b\uff0c$r = r_i\\ (> r)$ \u3067\u9759\u6b62\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3092\u8ab2\u3059\u3068\uff0c<\/p>\n

$$\\bar{u}^{\\mu} = \\left(\\frac{ \\sqrt{1 – \\frac{r_g}{r_i}}}{1 – \\frac{r_g}{r}},\u00a0 -\\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}, 0, 0\\right) $$<\/p>\n

\u3053\u306e\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u52d5\u5f84\u65b9\u5411\u5916\u5411\u304d\u306b\u653e\u51fa\u3055\u308c\u305f\u5149\u306e\u632f\u52d5\u6570 $\\bar{\\omega}$ \u306f<\/p>\n

\\begin{eqnarray}
\n\\bar{\\omega} &=& – k_{\\mu} \\bar{u}^{\\mu} \\\\
\n&=& – k_0 \\bar{u}^0 – k_1 \\bar{u}^1 \\\\
\n&=& \\omega_c \\frac{ \\sqrt{1 – \\frac{r_g}{r_i}}}{1 – \\frac{r_g}{r}} \\pm \\frac{\\omega_c}{1 – \\frac{r_g}{r}} \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}} \\\\
\n&=& \\frac{\\omega_c}{1 – \\frac{r_g}{r}} \\left(\\sqrt{1 – \\frac{r_g}{r_i}} \\pm \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right)
\n\\end{eqnarray}<\/p>\n

\u91cd\u529b\u5834\u4e2d\u3092\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306b\u3088\u308b\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c<\/h3>\n

\u89b3\u6e2c\u8005\u304c\u5149\u6e90\u306b\u8fd1\u3065\u304f\u5834\u5408<\/h4>\n

\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u5149\u6e90\u306b\u8fd1\u3065\u304f\u5834\u5408\u306f\uff0c\u4e0b\u56f3\u306e\u3088\u3046\u306b $r_g < r_1 < r< r_i$ \u3068\u306a\u308a\uff0c\u5149\u306f\u5916\u5411\u304d\uff0c\u3064\u307e\u308a\u8907\u53f7 \\(\\pm\\) \u306e \\(+\\) \u3092\u3068\u308b\u3002<\/p>\n

\"\"<\/p>\n

\u3057\u305f\u304c\u3063\u3066\uff0c$r = r_1$ \u306e\u5149\u6e90\u304b\u3089\u632f\u52d5\u6570 $\\omega_1$ \u3067\u653e\u51fa\u3055\u308c\u305f\u540c\u3058\u5149\u3092\uff0c\u96e2\u308c\u305f\u4f4d\u7f6e $r\\\u00a0 (> r_1)$ \u3067\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u5834\u5408\u3068\uff0c\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u5834\u5408\u3068\u3067\u306f\uff0c<\/p>\n

\\begin{eqnarray}
\n\\frac{\\frac{\\bar{\\omega}}{\\omega_1}}{\\frac{{\\omega}}{\\omega_1}} &=& \\frac{\\bar{\\omega}}{\\omega} \\\\
\n&=& \\frac{1}{\\sqrt{1 – \\frac{r_g}{r}}} \\left(\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right) > 1
\n\\end{eqnarray}<\/p>\n

\u3068\u306a\u308a\uff0c\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3057\u3066 $r = r_1$ \u306b\u3042\u308b\u5149\u6e90\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570 $\\bar{\\omega}$ \u306e\u307b\u3046\u304c\uff0c\u9759\u6b62\u89b3\u6e2c\u8005\u306e\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570 $\\omega$ \u3088\u308a\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306b\u3088\u3063\u3066\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\u7279\u306b\uff0c\u89b3\u6e2c\u8005\u304c\u5341\u5206\u9060\u65b9\u304b\u3089\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3092\u306f\u3058\u3081\u305f\u3068\u3059\u308b\u3068\uff0c\\(r_i \\rightarrow \\infty\\)\u00a0 \u3068\u3057\u3066<\/p>\n

$$\\frac{\\bar{\\omega}}{\\omega} \\simeq \\frac{1 +\u00a0 \\sqrt{\\frac{r_g}{r} }}{\\sqrt{1 – \\frac{r_g}{r}}}$$<\/p>\n

\u5ff5\u306e\u305f\u3081\uff0c\u3053\u306e\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3002<\/p>\n

\\begin{eqnarray}
\n\\frac{\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}}{\\sqrt{1 – \\frac{r_g}{r}}} &>&
\n\\frac{\\sqrt{1 – \\frac{r_g}{r_i}} }{\\sqrt{1 – \\frac{r_g}{r}}}\\\\
\n&=& \\frac{\\sqrt{1 – \\frac{r_g}{r} + \\left( \\frac{r_g}{r} – \\frac{r_g}{r_i}\\right)} }{\\sqrt{1 – \\frac{r_g}{r}}} \\\\
\n&>& \\frac{\\sqrt{1 – \\frac{r_g}{r} } }{\\sqrt{1 – \\frac{r_g}{r}}} \\\\
\n&=& 1 \\\\ \\ \\\\
\n\\therefore\\ \\ \\frac{\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}}{\\sqrt{1 – \\frac{r_g}{r}}} &>& 1
\n\\end{eqnarray}<\/p>\n

 <\/p>\n

\u89b3\u6e2c\u8005\u304c\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408<\/h4>\n

\u9006\u306b\uff0c\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408\u306f\uff0c\u4e0b\u56f3\u306e\u3088\u3046\u306b $r_g < r < r_1, \\ \\ r < r_i$ \u3068\u306a\u308a\uff0c\u5149\u306f\u5185\u5411\u304d\uff0c\u3064\u307e\u308a\u8907\u53f7 \\(\\pm\\) \u306e \\(-\\) \u3092\u3068\u308b\u3002<\/p>\n

\"\"<\/p>\n

\\begin{eqnarray}
\n\\frac{\\bar{\\omega}}{\\omega}
\n&=& \\frac{1}{\\sqrt{1 – \\frac{r_g}{r}}} \\left(\\sqrt{1 – \\frac{r_g}{r_i}} –\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right) \\\\
\n&=& \\frac{\\left(\\sqrt{1 – \\frac{r_g}{r_i}} –\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right)\\left(\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right)}{\\sqrt{1 – \\frac{r_g}{r}}\\left(\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right)} \\\\
\n&=& \\frac{\\left(1 – \\frac{r_g}{r_i}\\right) –\u00a0 \\left(\\frac{r_g}{r} – \\frac{r_g}{r_i}\\right)}{\\sqrt{1 – \\frac{r_g}{r}}\\left(\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}\\right)} \\\\
\n&=& \\frac{\\sqrt{1 – \\frac{r_g}{r}}}{\\sqrt{1 – \\frac{r_g}{r_i}} +\u00a0 \\sqrt{\\frac{r_g}{r} – \\frac{r_g}{r_i}}} < 1
\n\\end{eqnarray}<\/p>\n

\u3068\u306a\u308a\uff0c\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408\u306b\u306f\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306b\u3088\u308a\uff0c\u9759\u6b62\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570\u3088\u308a\u3082\u5c0f\u3055\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n

\u7279\u306b\uff0c\u89b3\u6e2c\u8005\u304c\u5341\u5206\u9060\u65b9\u304b\u3089\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3092\u306f\u3058\u3081\u305f\u3068\u3059\u308b\u3068\uff0c\\(r_i \\rightarrow \\infty\\)\u00a0 \u3068\u3057\u3066<\/p>\n

$$\\frac{\\bar{\\omega}}{\\omega} \\simeq \\frac{1 –\u00a0 \\sqrt{\\frac{r_g}{r} }}{\\sqrt{1 – \\frac{r_g}{r}}} = \\frac{\\sqrt{1 – \\frac{r_g}{r}}}{1 +\u00a0 \\sqrt{\\frac{r_g}{r} }}$$<\/p>\n

\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u3068\u306e\u6574\u5408\u6027<\/h3>\n

\u3055\u3066\uff0c\u672c\u30b5\u30a4\u30c8\u3067\u306f\u300c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u306b\u3088\u3089\u306a\u3044\u8d64\u65b9\u504f\u79fb\u306e\u7d71\u4e00\u7684\u7406\u89e3<\/a>\u300d\u306b\u304a\u3044\u3066\uff0c\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u306f\uff0c\uff08\u7279\u6b8a\u76f8\u5bfe\u8ad6\u3067\u306e\u307f\u6709\u52b9\u306a\uff09\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u4f7f\u308f\u305a\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n

\u5149\u6e90\u306b\u8fd1\u3065\u304f\u5834\u5408\u306e\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f<\/h4>\n

\u7279\u306b\uff0c\u5149\u6e90\u9759\u6b62\u7cfb\u3067\u306e\u632f\u52d5\u6570 \\(\\omega\\) \u3092 \\(\\omega_0\\) \uff0c\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u304c\u6e2c\u5b9a\u3059\u308b\u632f\u52d5\u6570 \\( \\bar{\\omega}\\) \u3092 \\(\\omega_{\\rm obs}\\) \u3068\u8868\u8a18\u3059\u308b\u3068\uff0c\u89b3\u6e2c\u8005\u304c3\u6b21\u5143\u7684\u306a\u901f\u3055 $V$ \u3067\u5149\u6e90\u306b\u8fd1\u3065\u304f\u5834\u5408\u306e\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f<\/p>\n

$$ \\omega_{\\rm obs} =\u00a0 \\omega_0 \\sqrt{\\frac{1+V}{1-V} } $$<\/p>\n

\u306f\uff0c\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u306e\u307f\u306a\u3089\u305a\uff0c\u305d\u306e\u5c0e\u51fa\u65b9\u6cd5\u306e\u4e00\u822c\u6027\u304b\u3089\u91cd\u529b\u304c\u3042\u308b\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u306a\u72b6\u6cc1\u306b\u304a\u3044\u3066\u3082\u540c\u69d8\u306b\u6709\u52b9\u3067\u3042\u308b\u3002<\/p>\n

\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e3\u6b21\u5143\u7684\u901f\u3055 $V$<\/h4>\n

\u52d5\u5f84\u5ea7\u6a19 $r$ \u306e\u5730\u70b9\u306e\u9759\u6b62\u89b3\u6e2c\u8005 $A$ \u304b\u3089\u307f\u308b\u3068\uff0c\u76ee\u306e\u524d\u3092\u901a\u904e\u3059\u308b\u77ac\u9593\u306e\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005 $B$ \u306e\u901f\u3055 $V$ \u306f\uff0c\u300c\u30b7\u30e5\u30d0\u30eb\u30c4\u30b7\u30eb\u30c8\u6642\u7a7a\u4e2d\u3092\u52d5\u5f84\u65b9\u5411\u306b\u81ea\u7531\u843d\u4e0b\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005<\/a>\u300d\u306b\u8a18\u8f09\u306e\u3088\u3046\u306b\uff0c4\u5143\u901f\u5ea6\u306e\u5408\u6210\u5247<\/p>\n

$$\\bar{u}^{\\mu} = \\frac{1}{\\sqrt{1 – V^2}} u^{\\mu} + \\frac{V}{\\sqrt{1 – V^2}} e^{\\mu} $$<\/p>\n

\u3092\u4f7f\u3046\u3068\uff0c\u305d\u308c\u305e\u308c\u306e4\u5143\u901f\u5ea6\u306e\u5185\u7a4d\u304c\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50\u3092\u8868\u3059\u3053\u3068<\/p>\n

$$\\frac{1}{\\sqrt{1-V^2}} = – u_{\\mu} \\bar{u}^{\\mu}$$<\/p>\n

\u304b\u3089 $V$ \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\uff0c<\/p>\n

\\begin{eqnarray}
\nV &=& \\frac{ \\sqrt{ \\frac{r_g}{r} – \\frac{r_g}{r_i} } }{ \\sqrt{1-\\frac{r_g}{r_i}} }
\n\\end{eqnarray}<\/p>\n

\u3068\u306a\u308b\u3002<\/p>\n

\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066…<\/h4>\n

\u4e0a\u8a18\u306e $V$ \u3092\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\uff0c<\/p>\n

\\begin{eqnarray}
\n\\frac{\\omega_{\\rm obs}}{ \\omega_0} &=&\u00a0 \\sqrt{\\frac{1+V}{1-V} } \\\\
\n&=& \\frac{1+V}{\\sqrt{1-V^2}} \\\\
\n&=& \\frac{1+\\frac{ \\sqrt{ \\frac{r_g}{r} – \\frac{r_g}{r_i} } }{ \\sqrt{1-\\frac{r_g}{r_i}} }}{\\sqrt{1-\\frac{ { \\frac{r_g}{r} – \\frac{r_g}{r_i} } }{{1-\\frac{r_g}{r_i}} }}}\\\\
\n&=&\\frac{{ \\sqrt{1-\\frac{r_g}{r_i}} }+{ \\sqrt{ \\frac{r_g}{r} – \\frac{r_g}{r_i} } }}{\\sqrt{{{1-\\frac{r_g}{r_i}} }-{ { \\left(\\frac{r_g}{r} – \\frac{r_g}{r_i}\\right) } }}}\\\\
\n&=&\\frac{{ \\sqrt{1-\\frac{r_g}{r_i}} }+{ \\sqrt{ \\frac{r_g}{r} – \\frac{r_g}{r_i} } }}{\\sqrt{{{1-\\frac{r_g}{r}} }}}
\n\\end{eqnarray}<\/p>\n

\u3068\u306a\u308a\uff0c\uff08\u5f53\u7136\u306e\u7d50\u679c\u3067\u306f\u3042\u308b\u304c\uff09\u4e0a\u8a18<\/a>\u3067\u6c42\u3081\u305f $\\displaystyle \\frac{\\bar{\\omega}}{\\omega}$ \u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u3002<\/p>\n

\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408\u3082\u540c\u69d8<\/h4>\n

\u901f\u3055 $V$ \u3067\u5149\u6e90\u304b\u3089\u9060\u3056\u304b\u308b\u5834\u5408\u3082\u540c\u69d8\u3067\uff0c<\/p>\n

$$ \\omega_{\\rm obs}=\u00a0 \\omega_0 \\sqrt{\\frac{1-V}{1+V} }$$<\/p>\n

\u306b\u901f\u3055 $V$ \u3092\u4ee3\u5165\u3059\u308c\u3070\u3088\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e16\u306e\u4e2d\u306e\u6559\u79d1\u66f8\u306b\u3088\u308b\u6a19\u6e96\u7684\u306a\u8aac\u660e\u3067\u306f\uff0c\u5149\u6e90\u3042\u308b\u3044\u306f\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u306b\u3088\u308b\u5149\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306f\uff0c\u91cd\u529b\u304c\u306a\u3044\u5834\u5408\u306e\u7279\u6b8a\u76f8\u5bfe\u8ad6\u7684\u72b6\u6cc1\u3067\u306e\u307f\u6709\u52b9\u3067\u3042\u308b\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u3092\u7528\u3044\u3066\u8aac\u660e\u3055\u308c\u3066\u3044\u305f\u3002\u91cd\u529b\u304c\u3042\u308b\u5834\u5408\u306f\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u5909\u63db\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u305f\u3081\uff0c\u5225\u9014\u7406\u5c48\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u4e00\u65b9\u3067\uff0c\u91cd\u529b\u8d64\u65b9\u504f\u79fb\u306e\u6a19\u6e96\u7684\u306a\u8aac\u660e\u306f\uff0c\u91cd\u529b\u5834\u4e2d\u306b\u304a\u3044\u3066\u5149\u6e90\u3082\u89b3\u6e2c\u8005\u3082\u9759\u6b62\u3057\u3066\u3044\u308b\u5834\u5408\u306b\u306e\u307f\u6709\u52b9\u3067\u3042\u3063\u305f\u3002<\/p>\n

\u3067\u306f\uff0c\u91cd\u529b\u5834\u4e2d\u3092\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306e\u89b3\u6e2c\u3059\u308b\u5149\u306e\u632f\u52d5\u6570\uff08\u3084\u6ce2\u9577\uff09\u3092\u8abf\u3079\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":3059,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-3390","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t