2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are Ittr= GM (r – 2GM) p3 GM r(r – 2GM) ' Itt = T00= −(r — 2GM), I= −(r – 2GM) sin² 0, 1 " ro ³r6 = ²,²0 = ro θφ rr pr= ro ™¹²,0 = ²/1, GM r(r – 2GM) ' Го = -sin cos 0, 1 tan 0 r Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are Ittr= GM (r – 2GM) p3 GM r(r – 2GM) ' Itt = T00= −(r — 2GM), I= −(r – 2GM) sin² 0, 1 " ro ³r6 = ²,²0 = ro θφ rr pr= ro ™¹²,0 = ²/1, GM r(r – 2GM) ' Го = -sin cos 0, 1 tan 0 r Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
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Transcribed Image Text:2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are
Ittr=
GM (r - 2GM)
p3
I 00
=
GM
r(r - 2GM)
"
− (r – 2GM), ¹
rr
=
Ir tt
−(r — 2GM) sin² 0,
=
Γ.
ro
1
=
2
Граф
9
=
го
["r
ro =
rr
1
GM
r(r – 2GM)
1
r
tan 0
Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
го
ΦΦ
=
9
- sin cos 0,
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