Periodical orbits and waveforms with spontaneous Lorentz symmetry-breaking in Kalb-Ramond gravity

TL;DR

This study investigates how spontaneous Lorentz symmetry-breaking in Kalb-Ramond gravity affects black hole geodesics, periodic orbits, and gravitational waveforms, providing potential observational signatures for future gravitational wave detectors.

Contribution

It introduces the impact of Lorentz symmetry-breaking parameter on geodesics, orbits, and gravitational waveforms in Kalb-Ramond gravity, a novel extension of black hole physics.

Findings

Lorentz-breaking parameter significantly alters geodesic structure.

Periodic orbits are affected by the parameter, changing their momentum and energy.

Gravitational waveforms exhibit distinctive features due to Lorentz symmetry-breaking.

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.