The regular cosmic string in Born-Infeld gravity

Rafael Ferraro and Franco Fiorini

Closed timelike curves and conical singularities contaminate the cylindrically symmetric vacuum solutions of general relativity. However both undesirable features can be avoided by means of an ultraviolet deformation of Einstein theory. We show that Born-Infeld gravity formulated in a spacetime endowed with absolute parallelism leads to a non-singular cosmic string. Although this vacuum solution behaves asymptotically as the respective general relativistic one, the conical singularity is removed because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. Moreover, the curvature invariants vanish at the minimal circle, so the curved solution joins two flat regions with different deficit angles. Remarkably, this very mechanism also removes the closed timelike curves.