# Signatures of noncommutativity in bar detectors of gravitational waves

## TL;DR

This paper investigates how noncommutative geometry could influence gravitational wave bar detectors, revealing potential detectable signatures and state transitions induced by noncommutative space structures.

## Contribution

It introduces a second-order analysis of noncommutative effects on bar detector responses, uncovering new state transitions absent in first-order approximations.

## Key findings

- Second-order terms induce transitions between ground and second excited states.
- Noncommutative length scale could be detectable via GW detectors.
- Enhanced understanding of noncommutative effects in quantum gravitational systems.

## Abstract

The comparison between the noncommutative length scale $\sqrt{\theta}$ and the length variation $\delta L=h L$, detected in the GW detectors indicate that there is a strong possibility to detect the noncommutative structure of space in the GW detector set up. We therefore explore how the response of a bar detector gets affected due to the presence of noncommutative structure of space keeping terms upto second order in the gravitational wave perturbation ($h$) in the Hamiltonian. Interestingly, the second order term in $h$ shows a transition between the ground state and one of the perturbed second excited states that was absent when the calculation was restricted only to first order in $h$.