  The relativistic quantum dynamics of a spinless charged particle interacting
with both Aharonov-Bohm and Coulomb-type potentials in the G\"odel-type
spacetime is considered. The dynamics of the system is governed by the
Klein-Gordon equation with interactions. We verify that it is possible to
establish a quantum condition between the energy of the particle and the
parameter that characterizes the vorticist of the spacetime. We rigorously
analyze the ground state of the system and determine the corresponding wave
functions to it.
