Fe b 19 99 Remark on the strength of singularities with a C 0 metric

Recently Nolan constructed a spherically-symmetric spacetime admitting a spacelike curvature singularity with a regular C metric. We show here that this singularity is in fact weak. In a recent paper Nolan [1] constructed a simple spherically-symmetric spacetime which includes a spacelike curvature singularity with a continuous (C) metric. The goal was to use this example to demonstrate that a curvature singularity with a C metric may be strong (according to the classification by Tipler [2] and by Ellis and Schmidt [3]). In this note we shall show that this singularity is in fact weak. We prove this by solving the second-order differential equation for the norm a of the radial Jacobi field, Eq. (n2) (hereafter the letter n before the equation number refers to Nolan’s paper [1]). We shall use here the notation of Ref. [1]. It will be assumed that the dynamics of a(t) and x(t) is correctly described by the corresponding secondorder differential equations, i.e. Eq. (n2) for a(t) and the equation preceding Eq. (n6) for x(t). Since f = f(x) (with x = u+ v), in Eq. (n2) we substitute fuv = f . We first show that a(t) = ẋe ≡ ā(t) (1)