[題目] Schwarzschild Metric
[領域]
廣義相對論、微分幾何
[來源]
作業
[題目]
Verify that Schwardzschild metric
2 2 2 2 2 2 2 2 2 2 2
c dτ = ds = c (1-a/r) dt -(1-a/r)^-1 dr -r dθ -r sin θdφ
is a solution of Einstein Eq in vacuum.
R = 0
μν
[瓶頸]
α
我知道 R = R ,只要把每項Christoffel symbol或g的微分求出代進去即可,
μν μαν
但問題是有太多項了,光 R 就有16個,每個 R 又各有4+3*3*2=22項(對g的微分),
μν μν
雖然有很多0跟重複的項,但還是相當麻煩。不知道有沒有比較簡潔的方法?
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