  A substantial fraction of stars can be found in wide binaries with projected
separations between $\sim10^2$ and $10^5\,\rm AU$. In the standard lore of
binary physics, these would evolve as effectively single stars that remotely
orbit one another on stationary Keplerian ellipses. However, embedded in their
Galactic environment their low binding energy makes them exceptionally prone to
perturbations from the gravitational potential of the Milky Way and encounters
with passing stars. Employing a fully relativistic $N$-body integration scheme,
we study the impact of these perturbations on the orbital evolution of wide
binaries along their trajectory through the Milky Way. Our analysis reveals
that the torques exerted by the Galaxy can cause large-amplitude oscillations
of the binary eccentricity to $1-e\lesssim10^{-8}$. As a consequence, the wide
binary members pass close to each other at periapsis, which, depending on the
type of binary, potentially leads to a mass transfer or collision of stars or
to an inspiral and subsequent merger of compact remnants due to
gravitational-wave radiation. Based on a simulation of $10^5$ wide binaries
across the Galactic field, we find that this mechanism could significantly
contribute to the rate of stellar collisions and binary black hole mergers as
inferred from observations of Luminous Red Novae and gravitational-wave events
by LIGO/Virgo/Kagra. We conclude that the dynamics of wide binaries, despite
their large mean separation, can give rise to extreme interactions between
stars and compact remnants.
