On Closed Timelike Curves and Warped Brane World Models

TL;DR

This paper explores the theoretical possibility of closed timelike curves in warped brane world models, analyzing the conditions under which causality violations might occur and explaining their absence in observable universe.

Contribution

It demonstrates that warped brane world models can theoretically produce CTCs but ultimately do not lead to observable causality violations due to the effective 4D field equations.

Findings

No asymptotic conical spacetime in brane models

Warped brane models can theoretically generate CTCs

Absence of cosmic strings in observations

Abstract

At first glance, it seems possible to construct in general relativity theory causality violating solutions. The most striking one is the Gott spacetime. Two cosmic strings, approaching each other with high velocity, could produce closed timelike curves. It was quickly recognized that this solution violates physical boundary conditions. The effective one particle generator becomes hyperbolic, so the center of mass is tachyonic. On a 5-dimensional warped spacetime, it seems possible to get an elliptic generator, so no obstruction is encountered and the velocity of the center of mass of the effective particle has an overlap with the Gott region. So a CTC could, in principle, be constructed. However, from the effective 4D field equations on the brane, which are influenced by the projection of the bulk Weyl tensor on the brane, it follows that no asymptotic conical space time is found, so no angle deficit as in the 4D counterpart model. This could also explain why we do not observe cosmic strings.