Bound Orbits and Gravitational Wave Radiation Around the Hairy Black Hole

TL;DR

This paper explores how the hair parameter affects bound orbits and gravitational wave signals around a hairy black hole, revealing minor effects consistent with observations but with potential long-term implications for gravitational wave detection.

Contribution

It systematically analyzes the influence of the hair parameter on geodesics, orbits, and gravitational waves, providing new insights into hairy black hole spacetime and observational constraints.

Findings

The hair parameter significantly impacts the event horizon.

Periodic orbit trajectories are similar to Schwarzschild black holes.

The hair parameter's effects on gravitational waves are subtle but may accumulate over time.

Abstract

The hairy black hole model provides a new theoretical framework for exploring phenomena in strong gravitational fields. This paper systematically investigates the influence of the hair parameter $\beta$ on the timelike geodesics of the regular hairy black hole, including the radius of the event horizon, the properties of bound orbits, and the characteristics of gravitational wave radiation over a single period. The study reveals that $\beta$ has a significant impact on the event horizon but only a minor effect on the innermost stable circular orbit(ISCO), the marginally bound orbit(MBO), and periodic orbits. Moreover, the trajectories of the periodic orbits are nearly identical to those of the Schwarzschild black hole. In addition, the parameter $\beta$ was constrained by simulating the precession observational data of the S2 star orbiting the supermassive black hole Sgr A*. The results indicate that the correction effects of $\beta$ comply with existing observational constraints, without providing stricter limitations. Furthermore, by considering periodic orbits as transitional orbits in the extreme-mass-ratio inspiral (EMRI) system, it is found that the presence of $\beta$ introduces subtle effects on the amplitude, phase, and period of the gravitational wave signal for a single orbit. Although these effects appear minor within a single cycle, they may accumulate into significant effects over long-term evolution. In the future, space-based gravitational wave detectors are expected to further investigate the properties of the hair parameter, enhancing our understanding of the spacetime structure and dynamical behavior of black holes.