Non-minimally coupled Einstein-Yang-Mills black holes: periodic orbits and gravitational wave radiation in extreme mass ratio systems

TL;DR

This paper explores how non-minimal coupling in Einstein-Yang-Mills black holes affects orbital dynamics and gravitational wave signals in extreme mass ratio inspirals, aiding future black hole classification via gravitational wave observations.

Contribution

It systematically analyzes the impact of magnetic charge and non-minimal coupling on orbits and gravitational waves in EYM black holes, revealing degeneracies and waveform modifications.

Findings

Decreased radii of marginally bound and innermost stable circular orbits with increasing parameters.

Shift of energy-angular momentum parameter space towards the left.

Enhanced gravitational wave amplitude and shortened periods with higher charge and coupling.

Abstract

Extreme mass ratio inspirals (EMRIs), as a core target for future space-based gravitational wave detection, offer crucial observational grounds for testing strong-field gravitational theories and classifying black holes through their orbital dynamics and gravitational wave radiation characteristics. This study systematically investigates the periodic orbit characteristics and gravitational wave radiation properties of EMRIs in the spacetime of a non-minimally coupled Einstein-Yang-Mills (EYM) black hole. The results show that as the magnetic charge parameter \(Q\) and the non-minimal coupling constant \(\xi\) increase, the radii of the marginally bound orbit (\(r_{\text{MBO}}\)) and the innermost stable circular orbit (\(r_{\text{ISCO}}\)) decrease significantly, with corresponding reductions in the orbital energy \(E\) and angular momentum \(L\). Furthermore, the allowable parameter space of energy and angular momentum (\(E\)-\(L\)) for bound orbits shifts towards the left. We then plot typical periodic orbits through orbit classification, finding that the non-minimal coupling effect suppresses the orbital contraction induced by the magnetic charge, leading to degeneracy of orbits with different \(Q\) values towards the Schwarzschild case, as well as phase shifts, amplitude enhancement, and period shortening in the gravitational waveforms with increasing \(Q\) and \(\xi\). These results provide theoretical predictions for distinguishing different black hole models through future gravitational wave observations.