  The unbounded center of mass (CM) energy of oppositely moving colliding
particles near horizon emerge also in 1+1- dimensional Horava-Lifshitz gravity.
This theory has imprints of renormalizable quantum gravity characteristics in
accordance with the method of simple power counting. Surpris- ingly the result
obtained is not valid for a 1- dimensional Compton- like process between an
outgoing photon and an infalling massless/ massive particle. It is possible to
achieve unbounded CM energy due to collision between infalling photons and
particles. The source of outgoing particles may be at- tributed to an explosive
process just outside the horizon for a black hole and the naturally repulsive
character for the case of a naked singularity. It is found that absence of
angular momenta in 1+1- dimensions does not yield unbounded energy for
collisions in the vicinity of naked singularities.
