  We explore an interesting connection between black hole shadow parameters and
the acceleration bounds for radial linear uniformly accelerated (LUA)
trajectories in static spherically symmetric black hole spacetime geometries of
the Schwarzschild type. For an incoming radial LUA trajectory to escape back to
infinity, there exists a bound on its magnitude of acceleration and the
distance of closest approach from the event horizon of the black hole. We
calculate these bounds and the shadow parameters, namely the photon sphere
radius and the shadow radius, explicitly for specific black hole solutions in
$d$-dimensional Einstein's theory of gravity, in pure Lovelock theory of
gravity and in the $\mathcal{F}(R)$ theory of gravity. We find that for a
particular boundary data, the photon sphere radius $r_{ph}$ is equal to the
bound on radius of closest approach $r_b$ of the incoming radial LUA trajectory
while the shadow radius $r_{sh}$ is equal to the inverse magnitude of the
acceleration bound $|a|_b$ for the LUA trajectory to turn back to infinity.
Using the effective potential technique, we further show that the same
relations are valid in any theory of gravity for static spherically symmetric
black hole geometries of the Schwarzschild type. Investigating the trajectories
in a more general class of static spherically symmetric black hole spacetimes,
we find that the two relations are valid separately for two different choices
of boundary data.
