具有共轭点的类光测地线的变分

VARIATION OF A NULL GEODESIC WITH CONJUGATE POINTS ON IT

在广义相对论中有一条重要的定理 :如果一条类光测地线γ0 (λ)在 (p ,q)间存在一点r沿γ0 (λ)共轭于 p ,那么γ0 (λ)的变分将给出连接 p ,q的类时曲线 .证明了这样得到的类时曲线趋于类光测地线时 ,它的固有加速度趋于无穷大 .

In general relativity, there is an important theorem that gives a null geodesic γ_0(λ ) with a point r in ( p,q ) conjugate to p along γ_0(λ ) , there will be a variation of γ_0(λ ) which will give a time-like curve from p to q . It is proved that the time-like curves coming from the above-mentioned variation have a proper acceleration approaching infinity as the time-like curve approaches the null geodesic.