Question

Transcribed Image Text:3. Consider the line element of the sphere of radius a:
ds² = a² (d0² + sin² 0 do²).
The only non-vanishing Christoffel symbols are
Ꮁ
06
sin cos 0,
го
θα
ГФ
1
фо
tan O'
гр
μν
2.90
a) Write down the metric and the inverse metric, and use the definition
1
гр
(µ9vo + v9μo – 8e9µ) = I
νμ
to reproduce the results written above for F
00
and ro
80°
[You can also check that the other
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