An alternative way to derive the geodesic deviation equation for rapidly diverging geodesics (Q2711465)

In 1926 T. Levi-Civita and J. L. Synge derived their celebrated equation of geodesic deviation under the assumption that the separation between the geodesics was small. Subsequently, \textit{D. E. Hodgkinson} [Gen. Relativ. Gravitation 3, 351-375 (1972; Zbl 0362.53013)] relaxed this condition to obtain a more general equation of geodesic deviation. In the present paper, the authors present a shorter and more transparent derivation of Hodgkinson's result. Contents include: an introduction; the derivation for rapidly diverging geodesics; and a discussion.