Constraining deviations from spherical symmetry using $ \gamma $-metric

The $\gamma$-spacetime metric is a static and axially symmetric vacuum solution of the Einstein equation. This spacetime represents a naked singularity and it has an extra parameter $\gamma$ which signifies deviations from spherical symmetry. In this work, we study the possibility of constraining the deformation parameter with astrophysical observations. We start with gravitational lensing in the weak and strong-field limit and calculate the respective deflection angles to show that only strong-field lensing observations will be able to constrain $\gamma$ independently. Later we study two other classical tests of gravity: Shapiro time delay and precession of perihelion. We show that, out of these two experiments, the deformation parameter affects the observables only in perihelion shift.