Exact solutions of vector bosons in the presence of the Aharonov-Bohm and Coulomb potentials in the gravitational field of topological defects in non-commutative space-time

In this paper, we obtain the exact solutions of Duffin-Kemmer-Petiau equation spin-1 in the presence of the Aharonov-Bohm and Coulomb potential in the gravitational field of cosmic string and a global monopole, we are study the DKP equation in commutative space-time, We separated the variables with the help of Wigner functions and the parity operator, We solved the system of the second order differential equation in the case of P = (−1) j+1 , but in the case of P = (−1) j we solved the system in j = 0. The spectrum of energy in the gravitational field of cosmic string and a global monopole are different, and the commutation relation of the angular momentum are obviously different from Pauli criterion in the Aharonov-Bohm effect, in spin-0 and spin-1 we have the non- commutativity energy by the perturbation theory, the energy is transition from commutative to non-commutative spac