[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/1438#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/1438","headline":"Penrose-Diagramm  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Penrose-Diagramm  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u7406\u8ad6\u7269\u7406\u5b66\u306b\u306fa\u304c\u3042\u308a\u307e\u3059 \u30da\u30f3\u30ed\u30fc\u30ba\u56f3 [\u521d\u3081] \uff08\u6570\u5b66\u8005\u304a\u3088\u3073\u7269\u7406\u5b66\u8005\u306e\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\uff09\u6642\u7a7a\uff08\u30a4\u30d9\u30f3\u30c8\uff09\u306e\u7570\u306a\u308b\u30dd\u30a4\u30f3\u30c8\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u8868\u30592\u6b21\u5143\u56f3\uff08\u56f31\u3092\u53c2\u7167\uff09\u3002\u3053\u308c\u306f\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u56f3\u306e\u62e1\u5f35\u3067\u3042\u308a\u3001\u90e8\u5c4b\u3068\u5782\u76f4\u306b\u6c34\u5e73\u306b\u767b\u9332\u3055\u308c\u3066\u304a\u308a\u3001\u5186\u9310\u306f\u6642\u7a7a\u306e\u7570\u306a\u308b\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u306b\u8868\u793a\u3055\u308c\u308b\u30e1\u30c8\u30ea\u30c3\u30af\u306f\u3001\u914d\u5ea7\u7570\u6027\u4f53\u5909\u63db\u306b\u3088\u3063\u3066\u5727\u7e2e\u3055\u308c\u308b\u305f\u3081\u3001\u7121\u9650\u306e\u6642\u9593\u3068\u7121\u9650\u306e\u90e8\u5c4b\u306e\u5ea7\u6a19\u304c2\u6b21\u5143\u4ed5\u4e0a\u3052\u30b5\u30d6\u30b9\u30da\u30fc\u30b9\u3068\u3057\u3066\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u56f3\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u6eb6\u6db2\uff08\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u3084\u305d\u306e\u4ed6\u306e\u7279\u7570\u70b9\u3001\u30a4\u30d9\u30f3\u30c8\u8996\u91ce\u3001\u6f38\u8fd1\u7684\u5e73\u5766\u6027\u306a\u3069\uff09\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u69cb\u9020\u3092\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 after-content-x4 \u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u4ee5\u4e0b\u304c\u6b63\u3057\u3044 \u30ab\u30fc\u30bf\u30fc – \u30da\u30f3\u30ed\u30fc\u30ba – \u30c7\u30a3\u30a2\u30b0\u30e9\u30e0 \u307e\u305f Penrose-Cartter-Diagramme \u3001\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u306b\u95a2\u4fc2\u306a\u304f\u3001\u305d\u308c\u3089\u306f\u7269\u7406\u5b66\u8005\u306e\u30d6\u30e9\u30f3\u30c9\u30f3\u30fb\u30ab\u30fc\u30bf\u30fc\u306b\u3088\u3063\u3066\u540c\u6642\u306b\u958b\u767a\u3055\u308c\u305f\u306e\u3067\u3001 [2] \u6642\u7a7a\u306e\u30e1\u30c8\u30ea\u30c3\u30af\u306b\u3064\u3044\u3066\u306f\u3001Minkowski\u56f3\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u62e1\u5f35\u3057\u307e\u3059\u3002 2\u6b21\u5143\u306e\u7269\u7406\u7684\u306a\u4e0b\u7740 M~{displaystyle textStyle","datePublished":"2022-02-14","dateModified":"2022-02-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/2\/2b\/Penrose-diagram-minkowski.svg\/langde-400px-Penrose-diagram-minkowski.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/2\/2b\/Penrose-diagram-minkowski.svg\/langde-400px-Penrose-diagram-minkowski.svg.png","height":"300","width":"400"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/1438","wordCount":7888,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u7406\u8ad6\u7269\u7406\u5b66\u306b\u306fa\u304c\u3042\u308a\u307e\u3059 \u30da\u30f3\u30ed\u30fc\u30ba\u56f3 [\u521d\u3081] \uff08\u6570\u5b66\u8005\u304a\u3088\u3073\u7269\u7406\u5b66\u8005\u306e\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\uff09\u6642\u7a7a\uff08\u30a4\u30d9\u30f3\u30c8\uff09\u306e\u7570\u306a\u308b\u30dd\u30a4\u30f3\u30c8\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u8868\u30592\u6b21\u5143\u56f3\uff08\u56f31\u3092\u53c2\u7167\uff09\u3002\u3053\u308c\u306f\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u56f3\u306e\u62e1\u5f35\u3067\u3042\u308a\u3001\u90e8\u5c4b\u3068\u5782\u76f4\u306b\u6c34\u5e73\u306b\u767b\u9332\u3055\u308c\u3066\u304a\u308a\u3001\u5186\u9310\u306f\u6642\u7a7a\u306e\u7570\u306a\u308b\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u56e0\u679c\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u306b\u8868\u793a\u3055\u308c\u308b\u30e1\u30c8\u30ea\u30c3\u30af\u306f\u3001\u914d\u5ea7\u7570\u6027\u4f53\u5909\u63db\u306b\u3088\u3063\u3066\u5727\u7e2e\u3055\u308c\u308b\u305f\u3081\u3001\u7121\u9650\u306e\u6642\u9593\u3068\u7121\u9650\u306e\u90e8\u5c4b\u306e\u5ea7\u6a19\u304c2\u6b21\u5143\u4ed5\u4e0a\u3052\u30b5\u30d6\u30b9\u30da\u30fc\u30b9\u3068\u3057\u3066\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u56f3\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u6eb6\u6db2\uff08\u30d6\u30e9\u30c3\u30af\u30db\u30fc\u30eb\u3084\u305d\u306e\u4ed6\u306e\u7279\u7570\u70b9\u3001\u30a4\u30d9\u30f3\u30c8\u8996\u91ce\u3001\u6f38\u8fd1\u7684\u5e73\u5766\u6027\u306a\u3069\uff09\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u69cb\u9020\u3092\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u306b\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u4ee5\u4e0b\u304c\u6b63\u3057\u3044 \u30ab\u30fc\u30bf\u30fc – \u30da\u30f3\u30ed\u30fc\u30ba – \u30c7\u30a3\u30a2\u30b0\u30e9\u30e0 \u307e\u305f Penrose-Cartter-Diagramme \u3001\u30ed\u30b8\u30e3\u30fc\u30fb\u30da\u30f3\u30ed\u30fc\u30ba\u306b\u95a2\u4fc2\u306a\u304f\u3001\u305d\u308c\u3089\u306f\u7269\u7406\u5b66\u8005\u306e\u30d6\u30e9\u30f3\u30c9\u30f3\u30fb\u30ab\u30fc\u30bf\u30fc\u306b\u3088\u3063\u3066\u540c\u6642\u306b\u958b\u767a\u3055\u308c\u305f\u306e\u3067\u3001 [2] \u6642\u7a7a\u306e\u30e1\u30c8\u30ea\u30c3\u30af\u306b\u3064\u3044\u3066\u306f\u3001Minkowski\u56f3\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u62e1\u5f35\u3057\u307e\u3059\u3002 2\u6b21\u5143\u306e\u7269\u7406\u7684\u306a\u4e0b\u7740 M~{displaystyle textStyle {widetilde {mathcal {m}}}}} \u6642\u9593\u3068\u90e8\u5c4b\u306e\u5ea7\u6a19\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 0\u3001 \u30d0\u30c4 1{displaystyle x^{0} ,, x^{1}} \u3068\u30e9\u30a4\u30f3\u8981\u7d20        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4d s~{displaystyle mathrm {d} {widetilde {s}}} \u30b3\u30f3\u30d5\u30a9\u30fc\u30de\u30fc\u5909\u63db\u306b\u3088\u3063\u3066 \u304a\u304a {displaystyle omega} \u3057\u305f\u304c\u3063\u3066\u3001\u300c\u975e\u7269\u7406\u7684\u300d\u3067 [\u521d\u3081] \u8986\u9762 M{displaystyle textStyle {mathcal {m}}} \u3068 d s = \u304a\u304a d s~{displaysyllle mathrm {d} s = omga\u3001mathrm {d} {widetilde {s} \u5ea7\u6a19\u306e\u5143\u306e\u6709\u9650\u307e\u305f\u306f\u7121\u9650\u306e\u9593\u9694\u306f\u3001\u65b0\u3057\u3044\u5ea7\u6a19\u306e\u6709\u9650\u9593\u9694\u3067\u793a\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u00b1 45 \u2218{displaystyle PM 45^{circ}} \u50be\u659c\u3057\u305f\u76f4\u7dda\u3002 Minkowski\u56f3\u306e\u3088\u3046\u306b\u3001\u524d\u65b9\u306e\u5149\u30b3\u30fc\u30f3\u5185\u306e\u4e00\u6642\u7684\u306a\u4e16\u754c\u306e\u7dda\u306f\u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u3067\u8d70\u308a\u307e\u3059\uff08\u4e16\u754c\u7dda\u306e\u63a5\u7dda\u306f\u5782\u76f4\u8ef8\u306b\u8fd1\u3044\u3002 \u00b1 45 \u2218{displaystyle PM 45^{circ}} a\uff09\u3002\u6709\u9650\u9593\u9694\u3067\u306e\u6709\u9650\u307e\u305f\u306f\u7121\u9650\u306e\u9593\u9694\u306e\u753b\u50cf\u306f\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u5316\u3068\u547c\u3070\u308c\u3001\u5883\u754c\u7dda\u306e\u5834\u5408\u3067\u3082\u30e1\u30c8\u30ea\u30c3\u30af\u306e\u56e0\u679c\u95a2\u4fc2\u306e\u5206\u6790\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059 \u30ea\u30e0 x0,x1\u2192\u00b1\u221eg \uff08 \u30d0\u30c4 0\u3001 \u30d0\u30c4 1\uff09\uff09 {displaystyle lim _ {x^{0} ,, x^{1} rightArrow pm infty} g\uff08x^{0}\u3001x^{1}\uff09} \u3002 [3]  \u56f32\uff1a\u5bfe\u5fdc\u3059\u308b\u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u306e\u69cb\u7bc9\u306e\u57fa\u790e\u3068\u3057\u3066\u306eMinkowski\u56f3\uff08\u56f31\u3092\u53c2\u7167\uff09\u3002 \u30da\u30f3\u30ed\u30fc\u30ba\u56f3\u306e\u69cb\u7bc9\u306b\u306f\u3001\u6b21\u306e\u30b9\u30ad\u30fc\u30e0\u304c\u3042\u308a\u307e\u3059\uff08\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u4ed8\u304d\u306e\u30df\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc\u30eb\u30fc\u30e0\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u56f32\u3092\u53c2\u7167\uff09\uff1a [4] \u6642\u9593\u3068\u90e8\u5c4b\u306e\u5ea7\u6a19\u304c\u9078\u629e\u3055\u308c\u3001\u4ee5\u4e0b\u306b\u5909\u63db\u3055\u308c\u307e\u3059\u3002\u2212\u221e\u221e2=\u2212dt2+dx2.{displaystyle mathrm {d} {widetilde {s}}^{2}=-mathrm {d} t^{2}+mathrm {d} x^{2}.}\u3053\u308c\u3089\u306e\u5ea7\u6a19\u306f\u3001\u30bc\u30ed\u5ea7\u6a19\u306b\u5909\u63db\u3055\u308c\u307e\u3059\u3002\u30bc\u30ed\u5ea7\u6a19\u306b\u306f\u3001\u30bc\u30ed\u306e\u9577\u3055\u306e\u5ea7\u6a19\u7dda\u306e\u63a5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u306f x0,x1{displaystyle x^{0} ,, x^{1}} \u5143\u306e\u5ea7\u6a19\u3068 \u03be0,\u03be1{displaystyle xi ^{0} ,, xi ^{1}} \u30bc\u30ed\u5ea7\u6a19\u3067\u3059 x0=x0(\u03be0,\u03be1),x1=x1(\u03be0,\u03be1),{displaystyle x^{0}=x^{0}(xi ^{0},xi ^{1}),quad x^{1}=x^{1}(xi ^{0},xi ^{1}),}\u305d\u308c\u304b gij\u2202xi\u2202\u03bem\u2202xj\u2202\u03bem=0(i,j,m=0,1).{displaystyle g_{ij}{frac {partial x^{i}}{partial xi ^{m}}}{frac {partial x^{j}}{partial xi ^{m}}}=0quad left(i,j,m=0,1right).}\u305f\u3068\u3048\u3070\u3001\u3042\u308a\u307e\u3059 u=t\u2212x,v=t+x{displaystyle u=t-x,quad v=t+x}\u3068 \u2212\u221e\u221e2=\u2212dudv.{displaystyle mathrm {d} {widetilde {s}}^{2}=-mathrm {d} u,mathrm {d} v.}\u65b0\u3057\u3044\u30bc\u30ed\u5ea7\u6a19\u306f\u3001\u9650\u3089\u308c\u305f\u9593\u9694\u3067\u3055\u3089\u306a\u308b\u5ea7\u6a19\u5909\u63db\u3067\u305d\u308c\u3089\u306e\u7121\u5236\u9650\u306e\u9593\u9694\u3092\u63cf\u304f\u3053\u3068\u306b\u3088\u3063\u3066\u5727\u7e2e\u3055\u308c\u307e\u3059\u3002p=arctan\u2061v,q=arctan\u2061u{displaystyle p=arctan v,quad q=arctan u}\u3068 \u2212\u03c02\u03c022=\u2212dpdqcos2\u2061pcos2\u2061q.{displaystyle mathrm {d} {widetilde {s}}^{2}=-{frac {mathrm {d} p,mathrm {d} q}{cos ^{2}p,cos ^{2}q}}.}\u30b3\u30f3\u30d1\u30af\u30c8\u5316\u3055\u308c\u305f\u30bc\u30ed\u5ea7\u6a19\u306f\u3001\u300c\u975e\u7269\u7406\u7684\u306a\u300d\u6642\u9593\u3068\u90e8\u5c4b\u306e\u5ea7\u6a19\u306b\u623b\u3055\u308c\u307e\u3059\uff08\u30b9\u30c6\u30c3\u30d72\u306e\u53cd\u8ee2\uff09\uff1aT=p+q,X=p\u2212q{displaystyle T=p+q,quad X=p-q}\u3068 \u2212\u03c0\u03c0,{displaystyle -pi 1cos2\u2061(T+X2)cos2\u2061(T\u2212X2)(dT2\u2212dX2){displaystyle mathrm {d} {widetilde {s}}^{2}=-{frac {1}{cos ^{2}left({frac {T+X}{2}}right),cos ^{2}left({frac {T-X}{2}}right)}}left(mathrm {d} T^{2}-mathrm {d} X^{2}right)}\u3068 ds2=\u2212(dT2\u2212dX2)=(cos2\u2061(T+X2)cos2\u2061(T\u2212X2))ds~2=\u03a9(T,X)ds~2.{displaystyle mathrm {d} {s}^{2}=-left(mathrm {d} T^{2}-mathrm {d} X^{2}right)=left(cos ^{2}left({frac {T+X}{2}}right),cos ^{2}left({frac {T-X}{2}}right)right)mathrm {d} {widetilde {s}}^{2}=Omega (T,X),mathrm {d} {widetilde {s}}^{2}.}\u4e2d\u8eab M{displaystyle {mathcal {m}}} \u9069\u7528\u53ef\u80fd\u3067\u3059 "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/1438#breadcrumbitem","name":"Penrose-Diagramm  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]