Schwarzschild Metrik, Kruskal Szekeres Koordinaten (G=M=c=1)

        Index: Implizit / Explizit / {t,r}⇔{u,w} / Plots


Input 1i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 1i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 2i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 2i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 3i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 3i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
Input 4i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 4i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
Input 5i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 5i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 6i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 6i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 7i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 7i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 8i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 8i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 9i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 9i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 10i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 10i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 11i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 11i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 12i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 12i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 13i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 13i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 14i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 14i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 15i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 15i:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

        ↑ Implizit / ↓ Explizit


Input 1e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 1e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 2e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 2e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 3e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 3e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
Input 4e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 4e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]
Input 5e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 5e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 6e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 6e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 7e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 7e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 8e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 8e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 9e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 9e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 10e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 10e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 11e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 11e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 12e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 12e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 13e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 13e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 14e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 14e:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

        ↑ Metrik / ↓ Transformation {t,r}⇔{u,w}


Input 1t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 2t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 2t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 3t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 4t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Output 4t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 5t:

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Input 6t:

krkptzpt_1.png

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]


Output 6t:

  ↓ Links: alle 4 Regionen mit Linien von konstantem r={4.08,3,2,0}, rechts: Linien von konstantem t=±{∞,4,3,2,1,0} und r={5,4,3,2,0}

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]       if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  ↓ Links: ein- und auslaufende Lichtwege, rechts: erreichbare Regionen Ⅰ und Ⅱ mit Lichtkegel auf u=3, w=1 (r=4.08) wie in Input 2t

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]       if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  ↓ Links: weißes Loch mit Singularität in der Vergangenheit, rechts: schwarzes Loch mit Singularität in der Zukunft

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]       if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

  ↑ Achsen: x=u, y=w

  if image doesn't load refresh with [F5] or force refresh with [ctrl]/[strg]+[F5]

Extras:

 nb Datei (Mathematica Code)
 mehr Diagramme in anderen Koordinaten

siehe auch:

 Rindler Koordinaten (beschleunigter Minkowski)

Tutorials:

 Trin Tragula
 Neil Turok
 Emil Akhmenov
 Eigenchris
 Leonard Susskind
 Kevin Brown
 Nick Lucid

Simon Tyran, Vienna         Index: [[ Metric Collection ]]     Backup: [[ Archived Version ]]     Main site: [[ yukterez.net ]]