https://doi.org/10.1140/epjc/s10052-026-15466-w
Regular Article - Theoretical Physics
Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
1
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, 310023, Hangzhou, China
2
United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology, 310023, Hangzhou, China
3
Key Laboratory of Cosmology and Astrophysics (Liaoning), College of Sciences, Northeastern University, 110819, Shenyang, China
4
Key Laboratory of Data Analytics and Optimization for Smart Industry (Ministry of Education), Northeastern University, 110819, Shenyang, China
5
Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, China
6
Institute of Theoretical Physics, Research Center of Gravitation, Lanzhou University, 730000, Lanzhou, China
a
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Received:
6
January
2026
Accepted:
18
February
2026
Published online:
17
March
2026
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.
© The Author(s) 2026
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