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Zbl 1063.53076
Tian, Guihua; Zheng, Zhao
The second variation of a null geodesic. (English)
[J] J. Math. Phys. 44, No. 12, 5681-5687 (2003). ISSN 0022-2488; ISSN 1089-7658/e

Summary: Confined to the second derivative of the variation of a null geodesic, the proper acceleration of the time-like curves obtained from the variation goes infinity as they approach the null geodesic except that the variation vector is a generalized Jacobi field on the null geodesic and the second variation $\beta_2$ is constant on the null geodesic.

MSC 2000:: *53C50 Lorentz manifolds, manifolds with indefinite metrics
53C22 Geodesics

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