  The accretion disks around black holes consist of infalling matter boosted
almost to the speed of light making collisions with opposite counterpart. This
is the rough picture occurring near black holes or other strongly gravitating
centers that produce observed phenomena such as astrophysical jets. A toy model
that can be considered imitating such a process is colliding null sources in
general relativity. We present such a simple model projected into the plane of
null coordinates that takes into account only neutral sources. We show that
even at such a simplified model, uncharged and non-rotating, it is possible to
obtain jet-like ejections albeit they lie below the horizon. In the present
study the spacetime consists of either one of i) a cloud of strings, ii) a
global monopole, iii) a particular model of bumblebee gravity, all described by
a similar class of stress-energy tensor. There are gravitational waves
accompanying the null sources and naturally collision of gravitational waves is
also taken into account. After the collision, the spacetime contains both null
and non-null sources, followed by trailing gravitational radiations. Locally
the interaction region of the colliding null-sources and gravitational waves is
isometric to the static background spacetime.
