The field equations for a time dependent cylindrical cosmic string coupled to gravity are reformulated in terms of geometrical variables defined on a $\mathrm{}(2+1)\mathrm{}$-dimensional spacetime by using the method of Geroch decomposition. Unlike the 4-dimensional spacetime the reduced case is asymptotically flat. A numerical method for solving the field equations which involves conformally compactifying the space and including null infinity as part of the grid is described. It is shown that the code reproduces the results of a number of vacuum solutions with one or two degrees of freedom. In the final section the interaction between the cosmic string and a pulse of gravitational radiation is briefly described. This is fully analyzed in the sequel.

• Received 30 June 2000

DOI:https://doi.org/10.1103/PhysRevD.63.024011