2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are GM (r - 2GM) Ittr= GM r(r - 2GM)' Iee (r2GM), Γ΄ Φ 00=- Itt = - (r - 2GM) sin² 0, == rø = 7/1/1 ГФо ro 00 Write down the geodesic equations for the Schwarzschild 2 [" Tr Tore= 1 GM r(r - 2GM)' го Φφ = - sin cos, 1 tan 0 spacetime and explain their relevance.
2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are GM (r - 2GM) Ittr= GM r(r - 2GM)' Iee (r2GM), Γ΄ Φ 00=- Itt = - (r - 2GM) sin² 0, == rø = 7/1/1 ГФо ro 00 Write down the geodesic equations for the Schwarzschild 2 [" Tr Tore= 1 GM r(r - 2GM)' го Φφ = - sin cos, 1 tan 0 spacetime and explain their relevance.
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The non-vanishing Christoffel symbols in the Schwarzschild spacetime are (see image aattached)
Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
Transcribed Image Text:2. The non-vanishing Christoffel symbols in the Schwarzschild spacetime are
GM(r - 2GM)
p3
It tr
=
GM
r(r - 2GM)'
I 00 = −(r — 2GM),
Itt =
I = −(r - 2GM) sin² 0,
1
ГФ
ro
"
7
I",
rr
rº = ²
ro
GM
r(r - 2GM)'
го
ΦΦ
1
гроф
tan 0
r
Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
==
sin cos 0,
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Step 1: Write down the geodesic equations for the Schwarzschild spacetime and explain their relevance.
VIEWStep 2: Derivation of Geodesic Equations in Schwarzschild Spacetime
VIEWStep 3: The geodesic equation for t
VIEWStep 4: Geodesic equation for r
VIEWStep 5: Geodesic equations for theta and phi
VIEWStep 6: Explanation of the geodesic equations
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