[Paper Review] Observing Geometrical Torsion

Stefano Lucat, Tomislav Prokopec|arXiv (Cornell University)|May 2, 2017

Pulsars and Gravitational Waves Research15 references3 citations

TL;DR

This paper proposes that conventional gravitational wave detectors like LIGO, Virgo, and LISA can detect dynamical torsion—specifically vector and mixed symmetric torsion—through distinct signatures in the relative acceleration of test masses, as governed by a generalized Jacobi equation. Unlike skew-symmetric torsion, which leaves no detectable signal, vector and mixed torsion produce unique, measurable effects that can be unambiguously distinguished from standard gravitational waves.

ABSTRACT

Dynamical (propagating) torsion can be observed by using conventional gravitational wave detectors such as LIGO, Virgo, LISA and bar detectors. We discuss specific signatures of different types of torsion, in particular those of vector and mixed symmetric torsion (skew symmetric torsion cannot be detected in this way). These signatures are specific to torsion and therefore they can be unambiguously distinguished from those of gravitational waves.

Motivation & Objective

• To investigate whether conventional gravitational wave detectors can detect dynamical torsion in spacetime geometry.
• To identify which components of torsion (vector, mixed symmetric, skew-symmetric) produce observable signals in such detectors.
• To establish a theoretical framework linking torsion components to measurable effects in the Jacobi equation for geodesic deviation.
• To demonstrate that torsion signatures are distinguishable from standard gravitational wave signals based on their unique dynamical response.

Proposed method

• Uses a generalized Jacobi equation that includes torsion and curvature contributions to model the relative acceleration of test masses along geodesics.
• Applies linearized gravity and torsion approximations around the Minkowski metric to simplify the equations for detection analysis.
• Decomposes the torsion tensor into three irreducible components: torsion trace vector $\mathcal{T}$, skew-symmetric torsion $\Sigma$, and mixed torsion $Q$ using Young tensor classification.
• Derives the leading-order contributions of each torsion component to the Jacobi field acceleration using covariant derivatives and the background Levi-Civita connection.
• Analyzes the response of interferometric detectors by modeling torsion waves as plane waves with specific polarizations analogous to gravitational waves.
• Considers the effective field theory of torsion trace from one-loop quantum corrections to matter fields, showing that $\mathcal{T}$ can become dynamical and propagate under certain conditions.

Experimental results

Research questions

• RQ1 Can conventional gravitational wave detectors detect dynamical torsion, and if so, which components of torsion are observable?
• RQ2 How do different irreducible components of torsion—vector, mixed symmetric, and skew-symmetric—affect the geodesic deviation of test masses?
• RQ3 What distinguishes the signatures of torsion waves from those of standard gravitational waves in interferometric detectors?
• RQ4 Under what conditions does the torsion trace become a light, long-range field capable of propagating over cosmological distances?
• RQ5 How does the coupling of torsion to scalar fields via Weyl symmetry influence the dynamics and detectability of torsion?

Key findings

• Skew-symmetric torsion ($\Sigma$) does not produce any detectable signal in conventional gravitational wave detectors, as its contribution to the Jacobi equation vanishes identically.
• The torsion trace vector ($\mathcal{T}$) induces a detectable signal proportional to $\overset{\circ}{\nabla}_J \mathcal{T}^\alpha + \dot{\gamma}^\alpha \overset{\circ}{\nabla}_J \mathcal{T}_{\dot{\gamma}}$, with distinct polarization responses in interferometers.
• Mixed symmetric torsion ($Q$) contributes via $-2\dot{\gamma}^\mu \frac{\overset{\circ}{D}}{D\tau} Q^\alpha_{\;\mu\rho} J^\rho$, producing unique, non-zero acceleration patterns in test masses.
• The torsion trace field $\mathcal{T}_\mu$ can be light and long-range if the coupling constant $\theta$ is large, enabling propagation over cosmological distances.
• The transverse component of $\mathcal{T}_\mu$ becomes massless in the limit $\theta \gg 1$, allowing it to propagate like a photon and be detectable by standard interferometers.
• The longitudinal component of $\mathcal{T}_\mu$ is very massive and short-ranged, making it undetectable at astrophysical scales, but still contributes to the field equations.