Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity

Abstract

This paper investigates the orbital dynamics and gravitational wave radiation characteristics of neutral test particles around a static spherically symmetric charged black hole (BH) in 4D Einstein-Gauss-Bonnet (4D-EGB) gravity theory. We analyze the dependence of the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO) on the Gauss-Bonnet coupling parameter $\hat{I}\pm$ and charge $Q$. The results indicate that the orbital radius, angular momentum, and energy all decrease with increasing $\hat{I}\pm$ or $Q$, with the corresponding bound orbit region shifting leftward in the $(E,L)$ parameter space. By combining observational data from the BH shadows of M87* and Sgr A* as well as the orbital precession of the S2 star, we constrain the model parameters and find that existing observations can limit the ranges of $\hat{I}\pm$ and $Q$ to a certain extent. Furthermore, we investigate the characteristics of periodic orbits corresponding to different rational numbers $q$ and the gravitational waveforms they excite, finding that variations in $\hat{I}\pm$ and $Q$ can lead to distinguishable differences in periodic orbit structures and gravitational wave phases. This study contributes to understanding the effects of Gauss-Bonnet corrections on BH spacetimes, and the results may provide theoretical references for future gravitational wave observations of extreme mass ratio inspirals (EMRIs).