Geodesics and periodic orbits around quantum-corrected black holes

Abstract

Abstract The orbital dynamics in a black hole spacetime can give us a chance to get deep insight into quantum gravity and fundamental physics. In this paper, we mainly focus on a massive particle’s motion around a quantum-corrected Schwarzschild black hole. In order to reveal some signatures of the adiabatic inspiral stage for probing the gravitational wave, the geodesics and periodic orbits around the black hole are investigated. It is found that bound orbits around the quantum-corrected Schwarzschild black hole have larger angular momentum and radius compared to the classic (Schwarzschild) black hole. Furthermore, by taking a taxonomy into account, periodic orbits for the massive particle are studied by a rational number with a triplet of integers. It suggests that the rational number increases with the increased of the energy of the massive particle. Besides, in the adiabatic inspiral stage, the particle’s periodic orbits around the quantum-corrected Schwarzschild black hole have higher energy in comparison to the ones in the classic black hole. These results demonstrated that the dynamical approach for the taxonomy enables us to distinguish the quantum-corrected Schwarzschild black hole from the classic black hole only by a massive particle’s periodic orbits.