  There exists a clear physical motivation for theoretical studies of the
vacuum instability related to the production of electron-positron pairs from a
vacuum due to strong external electric fields. Various nonperturbative (with
respect to the external fields) calculation methods were developed. Some of
these methods are based on possible exact solutions of the Dirac equation.
Unfortunately, there are only few cases when such solutions are known.
Recently, an approximate but still nonperturbative approach to treat the vacuum
instability caused by slowly varying $t$-electric potential steps (time
dependent external fields that vanish as $|t|\rightarrow\infty$), which does
not depend on the existence of the corresponding exact solutions, was
formulated in Ref. [S. P. Gavrilov, D. M. Gitman, Phys. Rev. D \textbf{95},
076013 (2017)]. Here, we present an approximate calculation method to treat
nonperturbatively the vacuum instability in arbitrary weakly inhomogeneous
$x$-electric potential steps (time-independent electric fields of a constant
direction that are concentrated in restricted space areas, which means that the
fields vanish as $|x|\rightarrow\infty$) in the absence of the corresponding
exact solutions. Defining the weakly inhomogeneous regime in general terms, we
demonstrate the universal character of the vacuum instability. This
universality is associated with a large density of states excited from the
vacuum by the electric field. Such a density appears in our approach as a large
parameter. We derive universal representations for the total number and current
density of the created particles. Relations of these representations with a
locally constant field approximation for Schwinger's effective action are
found.
