Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity

TL;DR

This paper investigates how periodic orbits around black holes in an extended theory of gravity influence gravitational wave signals, offering potential new ways to test deviations from general relativity.

Contribution

It introduces a detailed analysis of periodic orbits and gravitational waveforms in an effective field theory extension of general relativity, highlighting observable signatures of strong-field deviations.

Findings

Higher zoom numbers produce more complex gravitational wave substructures.

The properties of periodic orbits are characterized by three topological integers.

The study links orbital behavior to potential gravitational wave observations.

Abstract

The study of periodic orbits in extreme-mass-ratio inspirals is essential for understanding the dynamics of small bodies orbiting supermassive black holes. In this paper, we study the periodic orbits and their corresponding gravitational wave emissions within the framework of an effective field theory-based extension of general relativity (EFTGR), which incorporates higher-order curvature terms into the Einstein-Hilbert action. We start with a brief analysis of the modified black hole spacetime in EFTGR and examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. Focusing on the impact of the higher-order curvature terms in EFTGR, we examine the properties of periodic orbits, which are characterized by three topological integers $(z, w, v)$ that uniquely classify their trajectories. By analyzing these orbits within EFTGR, we aim to provide new insights into how strong-field deviations from general relativity may manifest in observable phenomena. 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. The results contribute to a clearer understanding of the dynamical features of EFTGR and open new avenues for probing black hole properties via gravitational wave detection.