Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes

TL;DR

This paper explores exotic solutions in General Relativity, such as traversable wormholes and warp drive spacetimes, focusing on their properties, the necessity of exotic matter, and implications for causality violations.

Contribution

It provides an extensive analysis of the physical features of exotic spacetime geometries and discusses their role as theoretical probes of general relativity's foundations.

Findings

Exotic spacetimes require matter that violates energy conditions.

Some solutions allow closed timelike curves, implying causality violations.

These geometries serve as theoretical tools to test general relativity's limits.

Abstract

The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely 'exotic matter,' involving a stress-energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. These solutions are primarily useful as 'gedanken-experiments' and as a theoretician's probe of the foundations of general relativity, and include traversable wormholes and superluminal 'warp drive' spacetimes. Thus, one may be tempted to denote these geometries as 'exotic' solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves. In this article, in addition to extensively exploring interesting features, in particular, the physical properties and characteristics of these 'exotic spacetimes,' we also analyze other non-trivial general relativistic geometries which generate closed timelike curves.