Traveling waves in strongly gravitating cosmic strings

We find the metric due to a traveling wave on a strongly gravitating cosmic string. This metric is one of the $\mathrm{pp}$ wave solutions to Einstein's equation. In the weak-field limit the metric reduces to the weak-field traveling-wave metric found by Vachaspati. The properties of the metric are examined and are found to agree with those properties proposed by Unruh et al. for strongly gravitating cosmic strings.