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We approach to the ortho-positronium (o-Ps) as a relativistic two-bodyproblem in $2+1$ dimensions in which o-Ps is composed of two-oppositely chargedparticles interacting via an attractive Coulomb force. In addition toseparation of center of mass and relative coordinates, mapping the backgroundinto the polar space-time gives possibility of construction of possible spineigen-states of o-Ps. This approach makes the energy spectrum complex in orderto describe o-Ps that can decay. From the complex energy expression, we findthe annihilation energy, binding energy and the life-time of o-Ps, in S state.

Annihilation energy and decay time of an ortho-Positronium