Testing quantum Einstein gravity via epicyclic oscillations around rotating black hole

Abstract

We consider the motion of test particles moving around a rotating black hole in the framework of quantum gravity and examine the influence of parameters of the model on the test particle motion. The black hole solution is characterized by four parameters, the mass $M$ of the black hole, the rotation parameter $a$ of the black hole, and two parameters $\alpha$ and $\beta$ of the quantum theory of gravity. We discuss the stability of equatorial circular orbits, and derive analytical solutions for the angular momentum and the corresponding energy for equatorial circular orbits. We also discuss the effective force acting on test particles. Furthermore, we discuss the epicyclic oscillations and derive the analytical expressions for the orbital, radial, and vertical frequencies as a function of the parameters of the underlying model. We also examine the Periastron frequency and Lense–Thirring precession. It is shown that the motion of particles around a rotating black hole in the background of quantum gravity is influenced by the black hole parameters.