Probing Cosmic Strings via Black Hole Quasinormal Modes in Gravitational Wave Astronomy

TL;DR

The paper addresses detecting cosmic strings via gravitational waves by examining how strings perturb Schwarzschild black hole quasinormal modes (QNMs). It develops a perturbative, Schrödinger-like framework with the tortoise coordinate and Regge–Wheeler potential, introducing perturbation potentials $V_{\rm UCS}$ and $V_{\rm CCS}$ to model uncharged and charged strings. Numerical analysis for a $10M_\odot$ black hole shows that extremely small perturbations with $\lambda$ as low as $10^{-10}$ (uncharged) or $10^{-7}$ (charged) imprint observable shifts, including eigenvalue center–splitting patterns and level repulsion, enabling potential inverse estimation of string energy $E_s$ and electromagnetic parameter $N$. The work suggests that future GW upgrades could enable cosmic-string detection or constraint via QNM ringdown spectroscopy, offering a new observational avenue beyond traditional signatures.

Abstract

Black holes, the simplest solution to Einstein's field equations, do not emit light, making their observations a major challenge for researchers. However, discovery of binary black holes (BBHs) in 2015 by LIGO has transformed the study of compact objects, with over 300 BBHs recorded, providing a new avenue for probing new physics. GWs remain a prominent and precise method of observing not only BBHs, but also dark matter and cosmic strings. Cosmic strings -- hypothetical one dimensional topological defects formed in the early universe, are yet to be observed, with multiple detection methods such as particle radiation, gravitational waves and lensing being proposed. Here we present a novel framework to search for cosmic strings by modeling them as perturbations within non-rotating black hole spacetime, focusing on their imprint on the spectrum of quasinormal modes (QNMs). Our numerical simulations identify a lower limit on perturbation strength, $λ\sim 10^{-10}$ for uncharged string and $λ\sim 10^{-7}$ for charged string, below which cosmic string effects become unobservable in QNM signals. By analyzing eigenvalue splitting and centers, we show that cosmic string properties impart distinct and detectable features to GW signals. Our results establish QNM analysis as a powerful, alternative observational strategy for constraining or detecting cosmic strings, and offer an inverse approach to estimate string energy or charge if a signal is detected. With upgrades in LIGO technologies and advanced multimessenger astronomy under development, these findings highlight new potential for detecting cosmic strings.

Figures (11)

• Figure 1: Perturbed vs Unperturbed eigenvalue comparison for uncharged cosmic string perturbation
• Figure 2: Eigenvalue splitting vs center eigenvalue for the case of uncharged cosmic string perturbation for different lambda values.
• Figure 3: Perturbed vs Unperturbed eigenvalue comparison for charged cosmic string perturbation
• Figure 4: Eigenvalue splitting vs center eigenvalue for the case of charged cosmic string perturbation for $\lambda \in (10^{-7},10^{-5})$
• Figure 5: Eigenvalue splitting vs center eigenvalue for the case of charged cosmic string perturbation for $\lambda \in (10^{-5},10^{-3})$