Gravitational Wave Signatures of Periodic Motion near Higher-Derivative Einstein-\AE ther Black Holes

TL;DR

This paper explores how higher-derivative modifications in Einstein-Ether gravity affect black hole spacetimes, leading to observable gravitational wave signatures from periodic orbits that could reveal deviations from general relativity.

Contribution

It derives corrected black hole metrics with quadratic curvature terms and analyzes their impact on gravitational waveforms from periodic orbits, highlighting potential observational signatures.

Findings

Higher-derivative corrections cause shifts in orbital dynamics.

Characteristic phase modulations appear in gravitational wave signals.

Frequency spectrum and amplitude are sensitive to coupling constants.

Abstract

Higher-derivative modifications of general relativity are generically expected from effective field theory approaches to quantum gravity, and they arise naturally in Lorentz-violating theories such as Einstein-Ether gravity. In this work, we investigate black hole spacetimes within Einstein-Ether theory supplemented by quadratic curvature corrections, including terms proportional to $R^2$, $R_{\mu\nu} R^{\mu\nu}$, and $R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$. We derive the corrected static, spherically symmetric metric perturbatively and examine its effects on the geodesic structure and gravitational wave emission. In particular, we analyze periodic timelike orbits in this background and compute the associated tensor-mode gravitational waveforms using the quadrupole approximation. Our results demonstrate that even small higher-derivative corrections can induce distinguishable shifts in the orbital dynamics and imprint characteristic phase modulations and harmonic deformations in the gravitational wave signal. These effects modify the frequency spectrum and amplitude envelope of $h_{+}$ and $h_{\times}$ in a manner sensitive to the coupling constants $\alpha$, $\beta$, and $\gamma$, and the Ether parameter $c_{13}$. The resulting signatures provide a potential observational window into ultraviolet deviations from general relativity and Lorentz symmetry in the strong-field regime.