Gravitational radiations from periodic orbits around Einstein-\AE{}ther black holes

TL;DR

This paper studies gravitational waves from periodic orbits around Einstein-er black holes, revealing how the er field alters waveforms and could be tested by future detectors.

Contribution

It introduces a detailed analysis of gravitational wave signatures from periodic orbits in Einstein-er black holes, highlighting the impact of the er field on waveform features.

Findings

Higher zoom numbers produce more complex waveforms.

The er field causes measurable deviations in gravitational wave signals.

Potential for future detectors to test Einstein-er gravity.

Abstract

In this work, we investigate the gravitational wave emission from the periodic orbital motion of a test particle around two specific types of black holes in Einstein-\AE{}ther theory, a modified gravity that locally breaks Lorentz symmetry while remaining consistent with theoretical and observational constraints through a careful selection of its four coupling constants $c_i$. Focusing on the impact of the \ae{}ther field, we examine the properties of periodic orbits, which are characterized by a set of three topological integers $(z, w, v)$ that uniquely classify their trajectories. We then calculate the gravitational waveforms generated by these periodic orbits, identifying potential observational signatures. Our analysis reveals a direct connection between the zoom-whirl orbital behavior of the small compact object and the gravitational waveforms it emits: higher zoom numbers lead to increasingly intricate waveform substructures. Moreover, the presence of the \ae{}ther field introduces significant modifications to these waveforms, imprinting measurable deviations that could be potentially tested or constrained by future space-based gravitational wave detectors.