1 5 2 D O C . 1 9 R E L AT I V I T Y L E C T U R E N O T E S
———————————————————————————————
Jakobis Satz.
anderer Beweis des Mult. Satzes
———————————————————————————————
Auflösung der linearen Gleichungen
Mult. aμν bμν
1
3!
----ñδλμν(δρστ)2(
- á a1ρbρλ)( a2σbσμ)( a3τbτν) =
e1λ e2μ e3ν
eμν
1
aμν bμν ⋅ aμαbαν =
dx′μ αμνdxν =
dV′ dxμa) ( αμνdxνα) ( αμν dxνα) ( αμν dV = = = =
dx″μ αμσdx′σ =
dx′σ αñβσνdxν á =
αμσ αñβσνdxν á =
dV″ αμσ dV′ αμσ αñβσν á dV = =
αμσβσν dV =
þ
ï
ý
ï
ü
Daraus der Satz.
αμν δρστδρ′σ′τ′aρρ′aσσ′aττ′
ρστ
å
=
Aρρ′ aρρ′ñaσσ′aττ′ á
στ
åδρστδρ′σ′τ′
=
Aρρ′aλρ′ δρστδρ′σ′τ′aλρ′aσσ′aττ′
στρ′
å
αμν δρλ = =
σ
Aρρ′
aμν
---------- - a(ρρ′) = aλρ′a
ρñ á
ρρ′) ( δλ
ρñ á
ρ
1 bezw.0.) ( =
aρ′λaρ′ρ
δλρ
=
ebens.
[p. 7]
dx′μ αμνdxν α(μρ) =
α(μρ)dx′μ δν ρdxν dxρ = =