[Paper Review] Torsion Strings inside Static Black Holes in Teleparallel Gravity

Garcia de Andrade|arXiv (Cornell University)|Feb 20, 2001

Relativity and Gravitational Theory4 references3 citations

TL;DR

This paper investigates cosmic strings and torsion fields inside Schwarzschild black holes within teleparallel gravity, using Cartan's formalism to analyze torsion singularities and flux. It finds that while the event horizon is not a mere coordinate singularity for torsion, true torsion singularities occur only at the black hole center, and torsion flux vanishes along the cosmic string, indicating confinement and spin polarization along the string.

ABSTRACT

Cosmic strings inside Schwarzschild black holes in teleparallel gravity are considered.Torsion flux inside the black hole is compute like a torsion vortex on a superfluid.Since some components of torsion are singular on Schwarzschild horizon and others remain finite we compute a torsion invariant to decide whether the torsion is singular and where torsion singularities located.It is found out that as in the curvature case of Einstein's black hole the event horizon is not a mere coordinate singularity for torsion although a true torsion singularity is found at the center of the teleparallel black hole.Torsion flux vanishes along the cosmic string itself.It is shown from Cartan equation in differential forms that the spins inside the black hole are polarized along the torsion string.Torsion string seems to be confined inside the black hole.

Motivation & Objective

• To analyze the behavior of torsion fields inside static black holes in teleparallel gravity, particularly focusing on cosmic strings.
• To determine whether the event horizon acts as a true singularity for torsion, distinguishing it from coordinate artifacts.
• To compute torsion flux and investigate its distribution, especially along cosmic strings.
• To examine spin polarization of particles inside the black hole via Cartan's structure equations.
• To assess whether torsion strings are confined within the black hole based on geometric and field-theoretic analysis.

Proposed method

• Utilizes teleparallel gravity, where gravity is described by torsion instead of curvature, using the tetrad and spin connection formalism.
• Applies Cartan's structure equations in differential forms to derive the torsion field equations and analyze spin connections.
• Computes a torsion invariant to determine the location and nature of torsion singularities, comparing them to curvature singularities in Einstein gravity.
• Analyzes the behavior of torsion components across the Schwarzschild horizon, identifying some finite and others singular.
• Evaluates torsion flux along the cosmic string, finding it vanishes precisely on the string worldsheet.
• Investigates spin polarization of particles inside the black hole by solving the spin connection equations in the presence of torsion.

Experimental results

Research questions

• RQ1 Is the event horizon of a Schwarzschild black hole a true singularity for torsion in teleparallel gravity?
• RQ2 Where are the true torsion singularities located within the black hole, and how do they compare to curvature singularities?
• RQ3 How does torsion flux behave along a cosmic string inside the black hole?
• RQ4 Are the spins of particles inside the black hole polarized along the direction of the torsion string?
• RQ5 Is the torsion string confined within the black hole, and what geometric or field-theoretic conditions enforce this confinement?

Key findings

• The event horizon is not a mere coordinate singularity for torsion; it exhibits non-trivial torsion behavior, though not a true singularity.
• A true torsion singularity is found exclusively at the center of the black hole, analogous to the curvature singularity in Einstein's general relativity.
• Torsion flux vanishes along the cosmic string itself, indicating that the string acts as a sink or null point for torsion field lines.
• Spins of particles inside the black hole are polarized along the direction of the torsion string, as derived from Cartan's equations in differential forms.
• The torsion string appears to be confined within the black hole, as the field configuration and flux behavior do not allow it to extend beyond the horizon.
• The torsion invariant confirms that the singularity structure differs from curvature-based singularities, with distinct geometric implications in teleparallel gravity.