Constraining deviations from spherical symmetry using γ -metric

Abstract

The $\ensuremath{\gamma}$-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 $\ensuremath{\gamma}$ 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 limits and calculate the respective deflection angles to show that only strong-field lensing observations will be able to constrain $\ensuremath{\gamma}$ 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.