Gravitational waveforms from periodic orbits around Gauss-Bonnet black holes

Abstract

Extreme mass-ratio inspirals (EMRIs) constitute one of the most promising probes of strong field gravity for future space borne gravitational-wave observatories. As a representative higher-curvature extension of General Relativity (GR), four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity is distinguished by its strictly linear geometric coupling. By this mathematical property, the pathological Fisher-matrix singularities that typically plague conventional modified black hole models are effectively evaded, thereby providing an ideal framework to test topological deviations from classical spacetimes. Through the classification of equatorial periodic orbits via an integer taxonomy $(z,w,v)$, it is demonstrated that even modest Gauss-Bonnet couplings ($\alpha \sim 0.1M^2$) imprint measurable geometric signatures onto the zoom-whirl architecture. Although the global conservative energy budget is shifted by a mere $\sim 0.2\%$, the short-range repulsive EGB core severely alters the strong field whirl dynamics, whereby a resolvable macroscopic dephasing of several radians per orbit is accumulated. Through semi-relativistic waveform modeling, it is revealed that this temporal compression manifests as a rigid, high-frequency stretching of the gravitational-wave harmonic comb -- a clean, amplitude-independent spectral signature ideally suited for detection by LISA, Taiji, and TianQin. A rigorous Fisher information analysis confirms that for a typical four-year observation at a signal-to-noise ratio of $\rho=20$, the marginalized error on the EGB coupling can be tightly bounded to $\sigma_\alpha \sim \mathcal{O}(10^{-6}) M^2$, with virtually negligible parameter degeneracy with the orbital eccentricity.