Curvature Invariants for Lorentzian Traversable Wormholes

TL;DR

This paper introduces a new method using curvature invariants to evaluate the traversability of Lorentzian wormholes, providing a coordinate-independent analysis of different wormhole metrics.

Contribution

It applies curvature invariants to assess wormhole traversability, extending a method previously used for black holes to various wormhole solutions.

Findings

Curvature invariants effectively identify traversable wormholes.

The method confirms the traversability of Morris-Thorne, thin-shell Schwarzschild, and exponential metric wormholes.

Invariant functions are successfully plotted for different wormhole metrics.

Abstract

A process for using curvature invariants is applied as a new means to evaluate the traversability of Lorentzian wormholes and to display the wormhole spacetime manifold. This approach was formulated by Henry, Overduin and Wilcomb for Black Holes in Reference [1]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates. The four independent Carminati and McLenaghan (CM) invariants are calculated and the non-zero curvature invariant functions are plotted. Three example traversable wormhole metrics (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric are investigated and are demonstrated to be traversable.