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

TL;DR

This paper explores how Gauss-Bonnet gravity modifications influence black hole orbital dynamics and gravitational wave signals, using observational data to constrain model parameters and analyzing periodic orbits and waveforms.

Contribution

It provides new insights into the effects of Gauss-Bonnet corrections on black hole orbits and gravitational waves, with observational constraints and analysis of periodic orbit structures.

Findings

Orbital radius, angular momentum, and energy decrease with increasing Gauss-Bonnet coupling and charge.

Observational data from BH shadows and S2 star precession constrain model parameters.

Variations in parameters lead to distinguishable differences in gravitational waveforms.

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 $\alpha$ and charge $Q$. The results indicate that the orbital radius, angular momentum, and energy all decrease with increasing $\alpha$ 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 $\alpha$ 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 $\alpha$ 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).