# Classical General Relativity Effects to Second Order in Mass, Spin, and Quadrupole Moment

## TL;DR

This paper extends classical general relativity calculations of light deflection, perihelion shift, time delay, and redshift to second order in mass, spin, and quadrupole moment using an approximate metric.

## Contribution

It introduces second order corrections to standard GR effects by combining Kerr and Erez-Rosen metrics, providing more precise theoretical predictions.

## Key findings

- Results agree with existing literature at first order.
- Extended calculations include second order terms in mass, spin, and quadrupole.
- Uses Mathematica for analytical derivations.

## Abstract

In this contribution, we calculate the light deflection, perihelium shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximaction of the Erez-Rosen spacetime. The results were obtained directly using Mathematica. 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.