Coexistence of vortices and antivortices in an abelian gauge theory

We present an Abelian field theory model that allows the coexistence of vortices and antivortices. Some of the interesting properties are that the magnetic flux is proportional to the difference of the numbers of vortices and antivortices but the energy is proportional to the sum of these numbers. In the context of cosmology, these vortices represent cosmic strings and antistrings with opposite magnetic charges. In addition to the above properties, we show that the total quantized curvature is proportional to the sum of the numbers of strings and antistrings which also determines the completeness of the gravitational metric.