Geodesic completeness in a wormhole spacetime with horizons

TL;DR

This paper demonstrates that certain wormhole spacetimes, despite having curvature divergences at the throat, are geodesically complete, challenging the usual link between divergences and singularities.

Contribution

It provides a detailed analysis of wormhole geometries in Palatini gravity coupled with Maxwell electrodynamics, showing geodesic completeness despite curvature divergences.

Findings

Wormhole solutions in Palatini gravity are geodesically complete.

Curvature divergences do not necessarily indicate spacetime singularities.

Explicit example of non-singular wormholes with divergences at the throat.

Abstract

The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.