Negative Energy Densities in Extended Sources Generating Closed Timelike Curves in General Relativity with and without Torsion

TL;DR

This paper investigates the conditions under which closed timelike curves appear near spinning sources in (2+1) and (3+1)-dimensional gravity, highlighting the role of energy densities, spin, and torsion.

Contribution

It demonstrates that in models with torsion, closed timelike curves only occur at unphysically high spin densities, and without torsion, they relate to unphysical heat flows, supporting their unphysical nature.

Findings

Closed timelike curves require unphysical spin densities with torsion.

Without torsion, CTCs are linked to unphysical heat flows.

Physical sources do not produce closed timelike curves.

Abstract

Near a spinning point particle in (2+1)-dimensional gravity (or near an infinitely thin, straight, spinning string in 3+1 dimensions) there is a region of space-time with closed timelike curves. Exact solutions for extended sources with apparently physically acceptable energy-momentum tensors, have produced the same exterior space-time structure. Here it is pointed out that in the case with torsion, closed timelike curves appear only for spin densities so high that the spin energy density is higher than the net effective energy density. In models without torsion, the presence of closed time-like curves is related to a heat flow of unphysical magnitude. This corroborates earlier arguments against the possibility of closed timelike curves in space-time geometries generated by physical sources.