  This paper studies how the static non-linear electromagnetic-vacuum spacetime
of a point nucleus with negative bare mass affects the self-adjointness of the
general-relativistic Dirac Hamiltonian for a test electron, without and with an
anomalous magnetic moment.
  The study interpolates between the previously studied extreme cases of a test
electron in (a) the Reissner--Weyl--Nordstr\"om spacetime (Maxwell's
electromagnetic vacuum), which supports a very strong curvature singularity
with negative infinite bare mass, and (b) the Hoffmann spacetime (Born or
Born--Infeld's electromagnetic vacuum) with vanishing bare mass, which features
the mildest possible curvature singularity.
  The main conclusion reached is: {on electrostatic spacetimes of a point
nucleus with a strictly negative bare mass} (which may be $-\infty$) essential
self-adjointness fails unless the radial electric field diverges sufficiently
fast at the nucleus and the anomalous magnetic moment of the electron is taken
into account.
  Thus on the Hoffmann spacetime with (strictly) negative bare mass the Dirac
Hamiltonian of a test electron, with or without anomalous magnetic moment, is
not essentially self-adjoint.
  All these operators have self-adjoint extensions, though, with the usual
essential spectrum $(-\infty,-\mEL c^2]\cup[\mEL c^2,\infty)$ and an infinite
discrete spectrum located in the gap $(-\mEL c^2,\mEL c^2)$
