关于广义Jacobi方程
On the generalized Jacobi equation
摘要：
标准教科书中的雅可比方程（测地线偏差方程）是通过将测地线方程围绕某些选定的测地线线性化而产生的，其中线性化是相对于坐标和速度完成的。由Hodgkinson在1972年引入并由Mashhoon等人进一步发展的广义Jacobi方程，如果线性化仅针对坐标而不是速度进行，则会出现。由此产生的方程已经研究了一些作者在某种程度上详细的类时测地线在洛伦兹流形。在这里，我们首先简要地考虑广义雅可比方程的仿射流形，没有一个度量，然后我们指定类光测地线的洛伦兹流形。我们通过考虑特殊的类光测地线（a）在史瓦西时空中和（b）在平面波时空中来说明后一种情况。
英文摘要：
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to the coordinates, but not with respect to the velocities. The resulting equation has been studied by several authors in some detail for timelike geodesics in a Lorentzian manifold. Here we begin by briefly considering the generalized Jacobi equation on affine manifolds, without a metric; then we specify to lightlike geodesics in a Lorentzian manifold. We illustrate the latter case by considering particular lightlike geodesics (a) in Schwarzschild spacetime and (b) in a plane-wave spacetime.
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