The second Bianchi identity is a differential curvature identity that is satisfied on any manifold with a smooth metric. If the metric of a Lorentzian manifold solves the Einstein equations, the twice contracted version of the second Bianchi identity implies the physical laws of energy and momentum conservation for the matter field permeating the spacetime. In this talk I define a distributional version of the twice-contracted second Bianchi identity, and show that it holds for spacetimes with time-like curvature singularities, provided that these singularities are in a precise sense not too strong. The momentum and energy balance laws that follow from this assertion could potentially be used to develop a theory, first envisioned by Weyl, in which worldlines of matter particles are identified with time-like singularities of an otherwise vacuum spacetime. As a first application, a large class of spherically symmetric static Lorentzian metrics with time-like one-dimensional singularities is identified, for which the identity holds. The proof uses the machinery of zero-area singularities (ZASS) and the notion of mass for them as defined by H. Bray. This is joint work with A. Burtscher and M. Kiessling.