Cosmic Strings in a Braneworld Theory with Metastable Gravitons

If the graviton possesses an arbitrarily small (but nonvanishing) mass, perturbation theory implies that cosmic strings have a nonzero Newtonian potential. Nevertheless in Einstein gravity, where the graviton is strictly massless, the Newtonian potential of a cosmic string vanishes. This discrepancy is an example of the van Dam–Veltman–Zakharov (VDVZ) discontinuity. We present a solution for the metric around a cosmic string in a braneworld theory with a metastable four-dimensional graviton. This theory possess those features that yield a VDVZ discontinuity in massive gravity, but nevertheless is generally covariant and classically self-consistent. Although the cosmic string in this theory supports a nontrivial Newtonian potential far from the cosmic string, one can recover the Einstein solution in a region near the cosmic string. That latter region grows proportionally to the evaporation length of the graviton (analogous to an inverse graviton mass), suggesting the lack of a VDVZ discontinuity in this theory. Moreover, the presence of scale dependent structure in the metric may have consequences for the search for cosmic strings through gravitational lensing techniques. E-mail: [email protected]