  We consider collision of two massive particles in the equatorial plane of an
axially symmetric stationary spacetime that produces two massless particles
afterwards. It is implied that the horizon is absent but there is a naked
singularity or another potential barrier that makes possible the head-on
collision. The relationship between the energy in the center of mass frame
$E_{c.m.}$ and the Killing energy $E$ measured at infinity is analyzed. It
follows immediately from the Wald inequalities that unbounded $E$ is possible
for unbounded $E_{c.m.}$ only. This can be realized if the spacetime is close
to the threshold of the horizon formation. Different types of spacetimes (black
holes, naked singularities, wormholes) correspond to different possible
relations between $E_{c.m.}$ and $E$. We develop a general approach that
enables us to describe the collision process in the frames of the stationary
observer and ZAMO (zero angular momentum observer). The escape cone and escape
fraction are derived. A simple explanation of the existence of the bright spot
is given. For the particular case of the Kerr metric, our results agree with
the previous ones found in M. Patil, T. Harada, K. Nakao, P.S. Joshi, and M.
Kimura, Phys. Rev. D 93, 104015 (2016).
