Orbital precession and Lense-Thirring effect of Horndeski rotating spacetimes

We study the precession features of a test particle and gyroscope attached to a stationary observer in Horndeski rotating spacetime. First, we study the precession orbit, Lense-Thirring (LT) precession as well as periastron precession frequencies of the test particle, which are helpful to test the strong gravity of the central object and to distinguish Horndeski rotating black holes from naked singularities. We find that both LT frequency and periastron precession frequency of Horndeski rotating black hole and naked singularity behave differently when the particle's orbit approaches the innermost stable circular orbit. Also, the effects of Horndeski parameter on the two precession frequencies are explored. Second, we investigate the spin precession of a test gyroscope in the Horndeski rotating spacetime by analyzing the LT frequency, the geodetic precession frequency, and the general spin precession frequency for a stationary observer in the spacetime. The angle, spin parameter and Horndeski parameter modify all these frequencies, which make the results shift from those in Kerr spacetimes. Furthermore, these precession frequencies for the Horndeski rotating black hole and naked singularity are distinguishable. In particular, as the observer gets close to the central object in an arbitrary direction, the frequencies of Horndeski black hole grow significantly and become divergent, while for naked singularity they are finite. These theoretical results in some sense provide a potential method to “detect” event horizon, and to distinguish Horndeski theory from Einstein's general relativity.