Can We Probe Spacetime Non-commutativity Through Tidal Deformability of Compact Objects?

TL;DR

This paper explores how spacetime non-commutativity affects the tidal deformability of compact objects and assesses the potential for gravitational wave observations to detect such effects, finding limitations with neutron and boson stars.

Contribution

It provides an analytical study of NC corrections to tidal deformability for various compact objects and evaluates their detectability via gravitational waves.

Findings

NC corrections converge at the black-hole-compactness limit

Neutron and boson stars are not suitable for constraining NC effects

Leading-order NC correction dominates near the black-hole limit

Abstract

We investigate the impact of spacetime non-commutativity on the tidal deformability of compact objects and explore the feasibility of detecting non-commutative (NC) effects through gravitational wave (GW) observations. We considered NC modifications to spacetime geometry based on de Sitter gauge theory of gravity and calculate their impact on tidal deformability. While several types of compact objects have been proposed as candidates for probing spacetime non-commutativity, particularly at the horizon scales, our study showed analytically that, for compact objects with non-singular metric at their surface (such as neutron stars and boson stars), the NC correction to their tidal deformability converge to a finite value at the black-hole-compactness limit, eliminating infinite enhancement at the horizon scales. We then compute the NC corrections for neutron stars and boson stars, considering several different models, and analyze their imprints on the GW signals. By comparing the results, we assess the scale of NC effects across different compactness regimes and discuss the conditions under which these NC effects can be amplified. While our findings suggest that the leading-order NC correction dominates the tidal deformability of a compact object near the black-hole-compactness limit, we demonstrate that neutron stars and boson stars are not viable candidates to constrain spacetime non-commutativity, while relying on the tidal deformability through GW observations.