9 6 D O C . 1 2 R E L A T I V I T Y L E C T U R E N O T E S
Energietensor des elektromagnetischen Feldes.
Physikalische Bedeutung
Allgemeiner Satz:
Für áabgeschlossenñ vollst. Syst.
Differentialform der Erhaltungssätze von Impuls-Energie
Übergang zu Integralform.
[35]
k1
∂T11
∂x1
---------- - –
∂T12
∂x2
---------- -
∂T13
∂x3
---------- -
∂T14
∂x4
---------- - – – – =
— — — — — — — — —
— — — — — — — — —
k4
∂T41
∂x1
---------- - –
∂T42
∂x2
---------- - ⋅
∂T44
∂x4
---------- - – – – =
þ
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ý
ï
ï
ï
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ü
kμ ⋅
∂T
∂xν
–------------μν
=
x
∂p11
∂x
---------- –
∂p12
∂y
----------
∂p13
∂z
----------
∂
1
∂t
------- - – – – =
— — — — — — —
— — — — — — —
i
c
--
l
∂sx
∂x
------- –
∂sy
∂y
-------
∂sz
∂z
-------
∂η
∂t
------ – – – =
Trs prs [u]
r
Tr4 = =
s[s]
i
c
--T[4s] = T44 –η =
kμ
∂T
∂xν
–------------μν
=
∂Tμν
∂xν
----------- -
å
0 =
[p. 10]
Tμν pδμν ρ0 dxμñuμuν á + = uν
dxν
ds
-------- = Σuν
2
1 =
–T44 p – ρ + =
μñ á ν
∂x
∂
pρμν ρ0uμuν) + (
∂p
∂x
νñ á μ
--------------- ρ0ñuμ-------------- á
∂ρ0uν
∂xν
uνρ-----------------
∂ ρñuμ á
∂xν
- + + 0 =
dρu
ds
------------μ