Rational orbits around 4D Einstein–Lovelock black holes

Abstract

The orbital dynamics in the strong gravitational field might present unique features of quantum gravity and high-dimensional theory. In this paper, a timelike particle’s periodic orbits around the 4-dimensional Einstein–Lovelock (4 D − EL) black holes are investigated by employing a classification of the zoom–whirl structure with a rational number q . It is found that these rational (periodic) orbits around 4 D − EL black holes have a higher or lower energy than the ones around Schwarzschild black holes during the inspiral stage of detecting the gravitational waves. It depends strongly on the sign of a coupling constant in the theory. These results might provide hints for distinguishing 4 D − EL black holes from Schwarzschild ones by using the orbital dynamical approach in the strong gravitational field.