[Paper Review] Cosmic Strings and Closed time-like curves in teleparallel gravity

Garcia de Andrade|arXiv (Cornell University)|Feb 22, 2001

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper investigates closed time-like curves (CTCs) in cosmic strings within teleparallel T4 gravity, showing that CTCs are forbidden unless a lower bound on angular momentum is satisfied. By matching an interior T4 solution with Cartan torsion to a GR vacuum solution, the study reveals that the core singularity behaves like a rotating point particle in 2+1 spacetime, strongly constraining time machine possibilities compared to Einstein-Cartan gravity.

ABSTRACT

Closed Time-like curves (CTC) in Cosmic strings in teleparallel T4 gravity are forbidden.This result shown here in T4 was shown by Soleng (Phys.Rev.D49 (1994)1124) also to be valid in Einstein-Cartan (EC) gravity.Here we show that in T4 to allow for CTC we are also led to a lower bound on the angular momentum of the cosmic string.This result is obtained by matching the interior T4 solution to a General Relativity (GR) vacuum solution.One of the main differences of the present report and the one by Soleng is that here the interior symmetric solution does not have necessary polarized spins but only Cartan torsion in the spirit of teleparallelism.Torsion flux is computed and it is show that the center of cylinder singularity corresponds to a 2 + 1 spacetime rotating point particle in T4.Therefore the possibility of building time machines seems to be strongly constraint than in the case of EC gravity.

Motivation & Objective

• To investigate the existence of closed time-like curves (CTCs) in cosmic strings within teleparallel T4 gravity.
• To determine whether CTCs can be allowed under specific physical conditions in the T4 framework.
• To compare constraints on CTC formation in T4 gravity with those in Einstein-Cartan gravity.
• To analyze the role of Cartan torsion and torsion flux in the interior solution of cosmic strings.
• To model the core singularity as a 2+1 spacetime rotating point particle in T4 gravity.

Proposed method

• Matching an interior T4 solution with Cartan torsion to a general relativity vacuum solution to model cosmic string spacetime.
• Computing torsion flux in the interior region to analyze geometric and physical properties of the solution.
• Applying the teleparallel formalism to describe gravity via torsion rather than curvature, focusing on symmetric solutions without polarized spins.
• Deriving conditions under which CTCs could emerge, leading to a lower bound on angular momentum.
• Analyzing the spacetime structure at the center of the cosmic string to identify its effective description as a rotating point particle in 2+1 dimensions.

Experimental results

Research questions

• RQ1 Can closed time-like curves exist in cosmic strings within teleparallel T4 gravity?
• RQ2 What constraints on angular momentum are required to allow CTCs in the T4 framework?
• RQ3 How does the presence of Cartan torsion affect the formation of CTCs compared to solutions with polarized spins?
• RQ4 How does the core singularity of the cosmic string behave in terms of effective spacetime geometry in T4 gravity?
• RQ5 How do the constraints on CTC formation in T4 gravity compare to those in Einstein-Cartan gravity?

Key findings

• Closed time-like curves (CTCs) in cosmic strings are forbidden in T4 gravity unless a lower bound on angular momentum is satisfied.
• The interior solution with only Cartan torsion—without polarized spins—still supports the formation of a 2+1 spacetime rotating point particle at the cylinder's center.
• Torsion flux is computed and found to be essential in characterizing the geometric structure of the cosmic string core.
• The lower bound on angular momentum required to allow CTCs in T4 gravity is derived through matching to a GR vacuum solution.
• The constraints on time machine formation in T4 gravity are significantly stronger than those in Einstein-Cartan gravity.