Geodetic precession and strong gravitational lensing in the dynamical Chern-Simons modified gravity

We have investigated the geodetic precession and the strong gravitational lensing in the slowly-rotating black hole in the dynamical Chern-Simons modified gravity theory. We present the formulas of the orbital period $T$ and the geodetic precession angle $\Delta\Theta$ for the timelike particles in the circular orbits around the black hole, which shows that the change of the geodetic precession angle with the Chern-Simons coupling parameter $\xi$ is converse to the change of the orbital period with $\xi$ for fixed $a$. We also discuss the effects of the Chern-Simons coupling parameter on the strong gravitational lensing when the light rays pass close to the black hole and obtain that for the stronger Chern-Simons coupling the prograde photons may be captured more easily, and conversely, the retrograde photons is harder to be captured in the slowly-rotating black hole in the dynamical Chern-Simons modified gravity. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the main observables for gravitational lensing in the strong field limit.Comment: 19 pages, 5 figures, more clarifications and references added, accepted for publication in Classical and Quantum Gravit