Detecting torsion from LISA and teleparallel gravity

TL;DR

This paper explores the possibility of detecting torsion in teleparallel gravity using gravitational wave detectors like LISA, proposing a gedanken experiment and estimating measurable effects based on Earth's torsion values.

Contribution

It introduces a novel method to detect torsion waves via gravitational wave detectors, linking torsion detection to existing GW technology and Earth's torsion measurements.

Findings

Estimated relative displacement of 10^{-21} for torsion waves.

Proposed LISA could indirectly detect torsion in T_4.

Utilizes Earth's known torsion value for detection feasibility.

Abstract

Torsion detection from totally skew symmetric torsion waves in the context of teleparallel gravity is discussed. A gedanken experiment to detect Cartan's contortion based on a circle of particles not necessarily spinning is proposed. It is shown that by making use of previous value of contortion at the surface of the Earth computed by Nitsch of $10^{-24} s^{-1}$ a relative displacement of $10^{-21}$ is obtained which is of the order of the gravitational wave of $10^{-3}Hz$. Since LISA has been designed to work in the mHz regime this GW detector could be used for an indirect detection of torsion in $T_{4}$.