Periodical orbits and waveforms with spontaneous Lorentz symmetry-breaking in Kalb–Ramond gravity
L. B. Ednaldo, José Tarciso S. S., Francisco S. N. Lobo, Manuel E. Rodrigues, Diego Rubiera-García, Luís F. Dias da Silva, Henrique A. Vieira
Abstract
Abstract In this paper, we study time-like geodesics around a spherically symmetric black hole in Kalb–Ramond (KR) gravity, characterized by the parameter l , which induces spontaneous Lorentz symmetry breaking. The geodesic equations and effective potential are derived to investigate the influence of l . We calculate the marginally bound orbits and innermost stable circular orbits, analyzing the parameter’s impact. Periodic orbits are computed numerically and classified within the standard taxonomy, revealing significant effects of l on their momentum and energy. Additionally, we explore an extreme mass ratio inspiral system under the adiabatic approximation to derive gravitational waveforms emitted by an object orbiting a supermassive black hole in KR gravity. These waveforms reflect the distinctive characteristics of periodic orbits and highlight the influence of l . With advancements in gravitational wave detection, these results offer insights into black holes influenced by Lorentz symmetry-breaking fields.