Download - WMAP of cosmic 3K microwaveradiation
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Hartmut Abele 1
WMAP of cosmic 3K microwaveradiation
Staus: 300000 years after BB
Kosmologie
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Hartmut Abele 2
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Hartmut Abele 3
Metrik im RMetrik im R22
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Hartmut Abele 4
Nikolaus von KuesNikolaus von Kues
Unde erit machina mundi quasi habens undique centrum et nullibi circumferentiam, quoniam eius circumferentiam et centrum esse deus, quid est undique et nullibi
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Hartmut Abele 5
KrümmungKrümmung
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Hartmut Abele 6
Gauss 1818 – 1826Gauss 1818 – 1826 Landvermessung Konigreich Hannover Landvermessung Konigreich Hannover
Brocken im Harz Inselberg im Thüringer
Wald Hoher Hacken bei
Göttingen
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Hartmut Abele 7
WMAP of cosmic 3K microwaveradiation
Staus: 300000 years after BB
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Hartmut Abele 8
RaumkrümmungRaumkrümmung
Gauss-Krümmung Riemann-
Krümmungstensor
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Hartmut Abele 9
Koordinaten, 2 dimensionalKoordinaten, 2 dimensional Kartesisch: ds2 = dx2 + dy2
Krümmung im Riemannschen Raum
s. Gravitation, U.E. Schröder, s. 30
2
2 2 211 12 222
ds g dx dx
ds g dx g dxdy g dy
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Hartmut Abele 10
Wichtige FormelnWichtige Formeln
Bernhard Riemann 1826 - 1866
Georgio Ricci-Curbastro 1853-1925
Elvin Bruno Christoffel 1829-1900
Tullio Levi-Civita1873-1941
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Hartmut Abele 11
EinsteingleichungEinsteingleichung
dh. die Expansion eines Volumens von Teilchen, die sich ursprünglich in Ruhe befinden, ist proportional zur Summe der Energiedichte und der 3 Druckkomponenten, s. J.C. Baez, “The Meaning of Einstein’s Equation”, http://arXiv.org/abs/gr-qc/0103044
18
2R Rg GT
18 ( )
2R G T Tg
4 ( )x y z
dG p p p
d
oder
oder
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Hartmut Abele 12
MaxwellMaxwell
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Hartmut Abele 13
R: time Sigma: space,
homogenious and isotropic
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Hartmut Abele 14
RWMRWM Robertson-Walker-Metrik
Flat case (R3 or more complicated )
Closed case
Open case
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Hartmut Abele 15
KosmologieKosmologie Robertson-Walker-Metrik
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Hartmut Abele 16
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Hartmut Abele 17
Friedmannsche DGLFriedmannsche DGL Einstein-Gleichung
Friedmann-Gleichungen