  The (twice-contracted) second Bianchi identity is a differential curvature
identity that holds on any smooth manifold with a metric. In the case when such
a metric is Lorentzian and solves Einstein's equations with an (in this case
inevitably smooth) energy-momentum-stress tensor of a "matter field" as the
source of spacetime curvature, this identity implies the physical laws of
energy and momentum conservation for the "matter field". The present work
inquires into whether such a Bianchi identity can still hold in a weak sense
for spacetimes with curvature singularities associated with timelike
singularities in the "matter field". Sufficient conditions that establish a
distributional version of the twice-contracted second Bianchi identity are
found. In our main theorem, a large class of spherically symmetric static
Lorentzian metrics with timelike one-dimensional singularities is identified,
for which this identity holds. As an important first application we show that
the well-known Reissner-Weyl-Nordstr\"om spacetime of a point charge does not
belong to this class, but that Hoffmann's spacetime of a point charge with
negative bare mass in the Born-Infeld electromagnetic vacuum does.
