Gravitational waveforms from periodic orbits around a charged black hole with scalar hair

TL;DR

This paper studies how scalar hair on charged black holes influences geodesic motion and gravitational wave signals, revealing detectable imprints that could be observed by future space-based detectors.

Contribution

It introduces a detailed analysis of scalar hair effects on orbits and gravitational waveforms from extreme mass-ratio inspirals around charged black holes.

Findings

Scalar hair shifts the positions of stable orbits.

Waveforms show distinct zoom-whirl patterns affected by scalar hair.

Scalar hair leaves observable imprints on gravitational wave signals.

Abstract

We investigate geodesic motion and gravitational-wave signatures of charged black holes with scalar hair. Using the effective potential approach, we analyze marginally bound orbits and innermost stable circular orbits, showing how their positions and energy thresholds are modified by the scalar hair parameter $r_B$. These results demonstrate scalar hair's role in altering the boundary of stable motion. We further explore periodic orbits characterized by rational frequency ratios, labeled by the index $(z,w,v)$, and quantify how scalar hair affects their orbital energy and angular momentum. Based on these orbital properties, we compute gravitational waveforms from extreme mass-ratio inspirals where a stellar-mass compact object orbits a supermassive charged black hole with scalar hair. Using the numerical kludge method, we generate waveforms that exhibit clear zoom-whirl patterns with morphology visibly affected by $r_B$. Our results show that scalar hair leaves distinguishable imprints on waveforms, suggesting future space-based detectors could probe deviations from classical black hole spacetimes through extreme mass-ratio inspirals observations.