一类类光测地线的加速度

Acceleration of a kind of null geodesic

类光测地线γ0 (λ)与二维类空超曲面 φ正交 ,λ为其仿射参量 .假如在类光测地线γ0 (λ)上存在一点r(r=γ0(λr) )共轭于类空超曲面 φ ,则对于γ0 (λ)上任一点q(q =γ0 (λq) )满足λq>λr,一定能把γ0 连续变形成一条从 φ到q的类时曲线 .当产生类时曲线的变分矢量场不是类光测地线上的广义Jacobi场时 ,这些类时曲线在趋于类光测地线时 。

When a null geodesic γ 0 ,orthogonal to a space_like two_surface φ ,is from φ to q with a point r∈(φ,q) conjugate to φ along γ 0(λ) ,there will be a variation of γ 0(λ) which will give time_like curves from φ to q .This is a well_known theory in the famous bood.When the variation vector is not a generalized Jacobi field on the null geodesic γ 0 ,the acceleration of these time_like curves approaches infinity as the time_like curves approach the null geodesic.