Classical general relativity effects to second order in mass, spin, and quadrupole moment

In this contribution, we calculate the light deflection, perihelion shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximation of the Erez-Rosen spacetime. The results were obtained directly using (Mathematica 2018 Wolfram Research, Inc., Version 11.3, Champaign). The results agree with the ones presented in the literature, but they are extended until second order terms of mass, angular momentum and mass quadrupole. The inclusion of the mass quadrupole is done by means of the metric; no expansion of the gravitational potential as in the parameterized post-Newtonian is required. (paper)