\u524d\u56de\u306f\u7dda\u5f62\u5316\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u304c0\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002
\u4eca\u56de\u306f\u539f\u70b9\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u8cea\u70b9\u3092\u60f3\u5b9a\u3057\u3066\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u3042\u305f\u3063\u3066\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u524d\u63d0\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
\u7dda\u5f62\u5316\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3057\u305f\u3002<\/p>\n\n\n\n
$$\n-\\frac{1}{2}\\Box\\psi_{\\mu\\nu}=\\frac{8\\pi G}{c^4}T_{\\mu\\nu}\n$$<\/p>\n\n\n\n
\u3053\u306e\u5f0f\u3088\u308a\u3001<\/p>\n\n\n\n
$$\n\\Box\\psi_{\\mu\\nu}=(-\\partial_t^2+\\Delta)\\psi_{\\mu\\nu}=-\\frac{16\\pi G}{c^4}T_{\\mu\\nu}\n$$<\/p>\n\n\n\n
\u3053\u3053\u3067\u767b\u5834\u3059\u308b$\\Delta$\u306f\u30e9\u30d7\u30e9\u30b9\u6f14\u7b97\u5b50\u3067\u3001$\\Delta\\equiv\\partial_x^2+\\partial_y^2+\\partial_z^2$\u3067\u3059\u3002<\/p>\n\n\n\n
$\\partial_t\\psi_{\\mu\\nu}=0$\u3068\u3044\u3046\u524d\u63d0\u6761\u4ef6\u3092\u8ab2\u3057\u305f\u306e\u3067\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001<\/p>\n\n\n\n
$$\n\\Delta\\psi_{\\mu\\nu}=-\\frac{16\\pi G}{c^4}T_{\\mu\\nu}\n$$<\/p>\n\n\n\n
\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\u539f\u70b9\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u8cea\u91cf$M$\u306e\u8cea\u70b9\u306b\u5bfe\u5fdc\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u30fb\u904b\u52d5\u91cf\u30c6\u30f3\u30bd\u30eb\u306f<\/p>\n\n\n\n
$$ \\left\\{ \\begin{aligned} &T_{00}=Mc^2 \\\\ &T_{\\mu\\nu}=0\\quad((\\mu,\\nu)\\neq(0,0)) \\end{aligned} \\right. $$<\/p>\n\n\n\n
\u306a\u306e\u3067\u3001<\/p>\n\n\n\n
$$ \\left\\{ \\begin{aligned} &\\Delta\\psi_{00}=-\\frac{16\\pi G}{c^4}\\cdot Mc^2=-\\frac{16\\pi GM}{c^2} \\\\ &\\Delta\\psi_{\\mu\\nu}=0\\quad((\\mu,\\nu)\\neq(0,0)) \\end{aligned} \\right. $$<\/p>\n\n\n\n
\u30ac\u30a6\u30b9\u306e\u767a\u6563\u5b9a\u7406\u3092\u7528\u3044\u3066$\\psi_{00}$\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
\u30ac\u30a6\u30b9\u306e\u767a\u6563\u5b9a\u7406<\/strong>(divergence theorem)<\/p>\n\n\n\n \u9762\u7a4d\u5206\u3068\u4f53\u7a4d\u5206\u306e\u95a2\u4fc2\u3092\u8868\u3059\u5f0f\u3067\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n $$\n\\int_S\\boldsymbol{E}\\cdot d\\boldsymbol{S}=\\int_V\\mathrm{div}\\boldsymbol{E}\\;dV\n$$<\/p>\n\n\n\n \u53f3\u8fba\u306b\u767b\u5834\u3059\u308b$\\mathrm{div}\\boldsymbol{E}$\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n $$\n\\mathrm{div}\\boldsymbol{E}=\\nabla\\cdot\\boldsymbol{E}=\\frac{\\partial E_x}{\\partial x}+\\frac{\\partial E_y}{\\partial y}+\\frac{\\partial E_z}{\\partial z}\n$$<\/p>\n\n\n\n \u30ac\u30a6\u30b9\u306e\u767a\u6563\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n $$\n\\int_V\\Delta\\psi_{00}dV=\\int_V\\nabla\\cdot\\nabla\\psi_{00}dV=\\int_S\\nabla\\psi_{00}dS\n$$<\/p>\n\n\n\n \u3053\u3053\u3067\u306e$V$\u306f\u534a\u5f84$r$\u306e\u7403\u3001$S$\u306f\u305d\u306e\u7403\u306e\u8868\u9762\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u3001$\\nabla=\\frac{\\partial}{\\partial x}+\\frac{\\partial}{\\partial y}+\\frac{\\partial}{\\partial z}$\u3092\u6975\u5ea7\u6a19\u3067\u8868\u3059\u3068\u3001<\/p>\n\n\n\n $$\n\\nabla=\\frac{\\partial}{\\partial r}+\\frac{1}{r}\\frac{\\partial}{\\partial\\theta}+\\frac{1}{r\\sin\\theta}\\frac{\\partial}{\\partial\\phi}\n$$<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002 \u8cea\u70b9\u306e\u307e\u308f\u308a\u306e\u91cd\u529b\u5834\u306f\u7403\u5bfe\u79f0\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u305f\u306e\u3067\u3001$\\frac{\\partial\\psi_{00}}{\\partial\\theta}=0$\u3001$\\frac{\\partial\\psi_{00}}{\\partial\\phi}=0$\u3068\u306a\u308b\u3053\u3068\u3088\u308a\u3001<\/p>\n\n\n\n $$\n\\nabla\\psi_{00}=\\frac{\\partial\\psi_{00}}{\\partial r}\n$$<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u308c\u3092\u5148\u7a0b\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n\n\n\n $$\n\\int_S\\nabla\\psi_{00}dS=\\int_S\\frac{\\partial\\psi_{00}}{\\partial r}dS=4\\pi r^2\\frac{\\partial\\psi_{00}}{\\partial r}\n$$<\/p>\n\n\n\n \u4e00\u65b9\u3001$\\int_V\\Delta\\psi_{00}dV=\\Delta\\psi_{00}$ (\u539f\u70b9\u4ee5\u5916\u306f\u771f\u7a7a\u3067\u3042\u308a\u3001$T_{00}=0$\u306e\u305f\u3081)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n $$\n4\\pi r^2\\frac{\\partial\\psi_{00}}{\\partial r}=-\\frac{16\\pi GM}{c^2}\n$$<\/p>\n\n\n\n \u3088\u308a\u3001<\/p>\n\n\n\n $$\n\\frac{\\partial\\psi_{00}}{\\partial r}=-\\frac{4GM}{c^2}\\frac{1}{r^2}\n$$<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n $$\n\\psi_{00}=\\int(-\\frac{4GM}{c^2})\\frac{1}{r^2}dr=\\frac{4GM}{c^2}\\frac{1}{r}+C_1\n$$<\/p>\n\n\n\n $C_1$\u306f\u5b9a\u6570\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u3001$h_{00}$\u3092\u8a08\u7b97\u3057\u3066\u307f\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002 $$\n\\begin{align*}\n h_{00}&=\\psi_{00}-\\frac{1}{2}\\psi\\eta_{00} \\\\\n &=\\psi_{00}-\\frac{1}{2}(-\\psi_{00})\\cdot(-1) \\\\\n &=\\frac{1}{2}\\psi_{00} \\\\\n &=\\frac{2GM}{c^2}\\frac{1}{r}+\\frac{C_1}{2}\n\\end{align*}\n$$<\/p>\n\n\n\n $r\\to\\infty$\u3067\u8a08\u91cf$g_{\\mu\\nu}=\\eta_{\\mu\\nu}+h_{\\mu\\nu}$\u304c\u5e73\u5766\u8a08\u91cf$\\eta_{\\mu\\nu}$\u306b\u4e00\u81f4\u3059\u308b\u3068\u4eee\u5b9a\u3057\u305f\u306e\u3067\u3001$h_{00}\\to 0$\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u3053\u3053\u307e\u3067\u306e\u8b70\u8ad6\u3092\u307e\u3068\u3081\u308b\u3068\u3001$h_{00}$\u306f\u3001<\/p>\n\n\n\n $$\nh_{00}=\\frac{2GM}{c^2}\\frac{1}{r}\n$$<\/p>\n\n\n\n \u305d\u308c\u4ee5\u5916\u306e\u6210\u5206\u306f\u3001<\/p>\n\n\n\n $$\n\\begin{align*}\n h_{ij}&=\\psi_{ij}-\\frac{1}{2}\\psi\\eta_{ij} \\\\\n &=-\\frac{1}{2}(-\\psi_{00})\\delta_{ij} \\\\\n &=\\frac{1}{2}\\psi_{00}\\delta_{ij} \\\\\n &=\\frac{2GM}{c^2}\\frac{1}{r}\\delta_{ij}\n\\end{align*}\n$$<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n $$\n\\begin{align*}\n ds^2&=(\\eta_{\\mu\\nu}+h_{\\mu\\nu})dx^{\\mu}dx^{\\nu} \\\\\n &=(-1+\\frac{2GM}{c^2}\\frac{1}{r})dt^2+(1+\\frac{2GM}{c^2}\\frac{1}{r})\\delta_{ij}dx^idx^j \\\\\n &=-(1-\\frac{2GM}{c^2}\\frac{1}{r})dt^2+(1+\\frac{2GM}{c^2}\\frac{1}{r})\\delta_{ij}dx^idx^j\n\\end{align*}\n$$<\/p>\n\n\n\n $\\delta_{ij}dx^idx^j=dx^2+dy^2+dz^2$\u306e\u90e8\u5206\u3082\u6975\u5ea7\u6a19\u3067\u8868\u73fe\u3057\u307e\u3059\u3002 $$ \\left\\{ \\begin{aligned} x&=r\\sin\\theta\\cos\\phi \\\\ y&=r\\sin\\theta\\sin\\phi \\\\ z&=r\\cos\\theta \\end{aligned} \\right. $$<\/p>\n\n\n\n \u307e\u305a\u3001\u305d\u308c\u305e\u308c\u306e\u5168\u5fae\u5206\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n $$ \\left\\{ \\begin{aligned} dx&=\\sin\\theta\\cos\\phi dr+r\\cos\\theta\\cos\\phi d\\theta-r\\sin\\theta\\sin\\phi d\\phi \\\\ dy&=\\sin\\theta\\sin\\phi dr+r\\cos\\theta\\sin\\phi d\\theta+r\\sin\\theta\\cos\\phi d\\phi \\\\ dz&=\\cos\\theta dr-r\\sin\\theta d\\theta \\end{aligned} \\right. $$<\/p>\n\n\n\n $dx^2,dy^2,dz^2$\u3092\u305d\u308c\u305e\u308c\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n $dx^2$\u306f<\/p>\n\n\n\n $$\n\\begin{align*}\n dx^2&=(\\sin\\theta\\cos\\phi dr)^2+(r\\cos\\theta\\cos\\phi d\\theta)^2+(r\\sin\\theta\\sin\\phi d\\phi)^2 \\\\\n &\\qquad+2rdrd\\theta\\sin\\theta\\cos\\theta\\cos^2\\phi-2rdrd\\phi\\sin^2\\theta\\cos\\phi\\sin\\phi \\\\\n &\\qquad-2r^2d\\theta d\\phi\\cos\\theta\\sin\\theta\\cos\\phi\\sin\\phi\n\\end{align*}\n$$<\/p>\n\n\n\n $dy^2$\u306f<\/p>\n\n\n\n $$\n\\begin{align*}\n dy^2&=(\\sin\\theta\\sin\\phi dr)^2+(r\\cos\\theta\\sin\\phi d\\theta)^2+(r\\sin\\theta\\cos\\phi d\\phi)^2 \\\\\n &\\qquad+2rdrd\\theta\\sin\\theta\\cos\\theta\\sin^2\\phi+2rdrd\\phi\\sin^2\\theta\\sin\\phi\\cos\\phi \\\\\n &\\qquad+2r^2d\\theta d\\phi\\cos\\theta\\sin\\theta\\sin\\phi\\cos\\phi\n\\end{align*}\n$$<\/p>\n\n\n\n $dz^2$\u306f<\/p>\n\n\n\n $$\ndz^2=(\\cos\\theta dr)^2+(r\\sin\\theta d\\theta)^2-2rdrd\\theta\\cos\\theta\\sin\\theta\n$$<\/p>\n\n\n\n \u306a\u306e\u3067\u3001$dx^2+dy^2+dz^2$\u306f<\/p>\n\n\n\n $$\n\\begin{align*}\n &dx^2+dy^2+dz^2 \\\\\n &=(\\sin\\theta\\cos\\phi dr)^2+(\\sin\\theta\\sin\\phi dr)^2 \\\\\n &\\qquad+(r\\cos\\theta\\cos\\phi d\\theta)^2+(r\\cos\\theta\\sin\\phi d\\theta)^2 \\\\\n &\\qquad+(r\\sin\\theta\\sin\\phi d\\phi)^2+(r\\sin\\theta\\cos\\phi d\\phi)^2 \\\\\n &\\qquad+2rdrd\\theta\\sin\\theta\\cos\\theta\\cos^2\\phi+2rdrd\\theta\\sin\\theta\\cos\\theta\\sin^2\\phi \\\\\n &\\qquad+(\\cos\\theta dr)^2+(r\\sin\\theta d\\theta)^2-2rdrd\\theta\\cos\\theta\\sin\\theta \\\\\n &=\\sin^2\\theta dr^2+r^2\\cos^2\\theta d\\theta^2+r^2\\sin^2\\theta d\\phi^2+2rdrd\\theta\\sin\\theta\\cos\\theta \\\\\n &\\qquad+\\cos^2\\theta dr^2+r^2\\sin^2\\theta d\\theta^2-2rdrd\\theta\\cos\\theta\\sin\\theta \\\\\n &=dr^2(\\sin^2\\theta+\\cos^2\\theta)+r^2d\\theta^2(\\cos^2\\theta+\\sin^2\\theta)+r^2\\sin^2\\theta d\\phi^2 \\\\\n &=dr^2+r^2d\\theta^2+r^2\\sin^2\\theta d\\phi^2 \\\\\n &=dr^2+r^2(d\\theta^2+\\sin^2\\theta d\\phi^2)\n\\end{align*}\n$$<\/p>\n\n\n\n \u3053\u308c\u3088\u308a\u3001<\/p>\n\n\n\n $$\n\\begin{align*}\n ds^2&=-(1-\\frac{2GM}{c^2}\\frac{1}{r})dt^2+(1+\\frac{2GM}{c^2}\\frac{1}{r})\\delta_{ij}dx^idx^j \\\\\n &=-(1-\\frac{2GM}{c^2}\\frac{1}{r})dt^2 \\\\\n &\\qquad +(1+\\frac{2GM}{c^2}\\frac{1}{r})(dr^2+r^2(d\\theta^2+\\sin^2\\theta d\\phi^2))\n\\end{align*}\n$$<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u3001\u52d5\u5f84\u5ea7\u6a19$r$\u3092\u5468\u534a\u5f84$\\rho$\u306b\u5207\u308a\u66ff\u3048\u307e\u3059\u3002<\/p>\n\n\n\n $$\n(1+\\frac{2GM}{c^2}\\frac{1}{r})r^2(d\\theta^2+\\sin^2\\theta d\\phi^2)=\\rho^2(d\\theta^2+\\sin^2\\theta d\\phi^2)\n$$<\/p>\n\n\n\n \u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n $$\n\\rho^2=(1+\\frac{2GM}{c^2}\\frac{1}{r})r^2\n$$<\/p>\n\n\n\n \u3088\u308a\u3001<\/p>\n\n\n\n $$\n\\rho=r\\sqrt{1+\\frac{2GM}{c^2}\\frac{1}{r}}\n$$<\/p>\n\n\n\n \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n $\\frac{2GM}{c^2}\\frac{1}{r}\\approx 0$\u3068\u307f\u306a\u3059\u3068\u3001$\\rho\\approx r$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n $$\n\\begin{align*}\n ds^2&=-(1-\\frac{2GM}{c^2}\\frac{1}{r})dt^2 \\\\\n &\\qquad +(1+\\frac{2GM}{c^2}\\frac{1}{r})(dr^2+r^2(d\\theta^2+\\sin^2\\theta d\\phi^2)) \\\\\n &\\approx -(1-\\frac{2GM}{c^2}\\frac{1}{\\rho})dt^2 \\\\\n &\\qquad +(1+\\frac{2GM}{c^2}\\frac{1}{\\rho})d\\rho^2+\\rho^2(d\\theta^2+\\sin^2\\theta d\\phi^2) \\\\\n &\\approx -(1-\\frac{2GM}{c^2}\\frac{1}{\\rho})dt^2+\\frac{d\\rho^2}{1-\\frac{2GM}{c^2}\\frac{1}{\\rho}}+\\rho^2(d\\theta^2+\\sin^2\\theta d\\phi^2)\n\\end{align*}\n$$<\/p>\n\n\n\n \u6700\u5f8c\u306e\u884c\u306e\u7b2c2\u9805\u306b\u3064\u3044\u3066\u306f\u3001$\\frac{1}{1-x}$\u3092\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3059\u308b\u3068$1+x+\\mathcal{O}(x^2)$\u3068\u306a\u308b\u3053\u3068\u3088\u308a\u3001$1+x\\approx\\frac{1}{1-x}$\u3068\u3044\u3046\u8fd1\u4f3c\u3092\u884c\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u3053\u3053\u3067\u306f\u6642\u7a7a\u306e\u6b6a\u307f\u304c\u5c0f\u3055\u3044($\\frac{2GM}{c^2}\\frac{1}{r}\\ll 1$)\u3068\u4eee\u5b9a\u3057\u3066\u8a08\u91cf\u3092\u5c0e\u51fa\u3057\u307e\u3057\u305f\u304c\u3001\u5b9f\u306f\u3001\u91cd\u529b\u5834\u304c\u5f37\u3044($\\frac{2GM}{c^2}\\frac{1}{r}\\approx 1$)\u5834\u5408\u3067\u3082\u3001\u3053\u306e\u8a08\u91cf\u306f\u305d\u306e\u307e\u307e\u3067\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u771f\u7a7a\u89e3\u306b\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002 $$\nds^2=g_{\\mu\\nu}dx^{\\mu}dx^{\\nu}=-f(r)dt^2+\\frac{dr^2}{f(r)}+r^2d\\Omega_{\\rm{II}}^2\n$$<\/p>\n\n\n\n $f(r)$\u306f<\/p>\n\n\n\n $$\nf(r)=1-\\frac{r_s}{r}\\equiv 1-\\frac{2GM}{c^2}\\frac{1}{r}\n$$<\/p>\n\n\n\n \u3053\u3053\u306b\u51fa\u3066\u304f\u308b$r_s=\\frac{2GM}{c^2}$\u3092\u30b7\u30e5\u30ef\u30eb\u30c4\u30b7\u30eb\u30c8\u534a\u5f84<\/strong>(Schwarzschild radius)\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n $d\\Omega_{\\rm{II}}^2$\u306f<\/p>\n\n\n\n $$\nd\\Omega_{\\rm{II}}^2\\equiv d\\theta^2+\\sin^2\\theta d\\phi^2\n$$<\/p>\n\n\n\n \u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u524d\u56de\u306f\u7dda\u5f62\u5316\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u304c0\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u4eca\u56de\u306f\u539f\u70b9\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u8cea\u70b9\u3092\u60f3\u5b9a\u3057\u3066\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002 \u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u3042\u305f\u3063\u3066\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u524d\u63d0\u3068\u3057\u307e\u3059\u3002 \u7dda\u5f62\u5316\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-543","post","type-post","status-publish","format-standard","hentry","category-9","category-10"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=543"}],"version-history":[{"count":12,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/543\/revisions"}],"predecessor-version":[{"id":1612,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/543\/revisions\/1612"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
\u5c0e\u51fa\u306f\u5272\u611b\u3057\u307e\u3059\u304c\u3001\u6c17\u306b\u306a\u308b\u65b9\u306f\u5404\u81ea\u3067\u8abf\u3079\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n
$h_{\\mu\\nu}=\\psi_{\\mu\\nu}-\\frac{1}{2}\\psi\\eta_{\\mu\\nu}$\u3067\u3001$\\psi=\\eta^{\\mu\\nu}\\psi_{\\mu\\nu}=\\eta^{00}\\psi_{00}=-\\psi_{00}$\u306a\u306e\u3067\u3001<\/p>\n\n\n\n
\u3053\u306e\u3053\u3068\u3088\u308a\u3001$C_1=0$\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\u4e09\u6b21\u5143\u306e\u6975\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
\u3053\u306e\u89e3\u3092\u30b7\u30e5\u30ef\u30eb\u30c4\u30b7\u30eb\u30c8\u89e3<\/strong>(Schwarzschild solution)\u3068\u547c\u3073\u307e\u3059\u3002
\u30b7\u30e5\u30ef\u30eb\u30c4\u30b7\u30eb\u30c8\u89e3\u3092\u6539\u3081\u3066\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n