We consider geodesics of massive and massless test particles in the gravitational field of a static and axisymmetric compact object described by the quadrupolar metric (q-metric), which is the simplest generalization of the Schwarzschild metric, containing an independent quadrupole parameter q. We analyze the effective potential profile and calculate the orbital parameters and capture cross-sections of test particles in this spacetime. Moreover, we derive the explicit expression for the escape angle of photons as a function of the quadrupole parameter. All the results reduce in the corresponding limit of vanishing quadrupole to the well-known case of the Schwarzschild spacetime. We argue that our results could be used to investigate realistic compact objects such as white dwarfs and neutron stars.
@article{arxiv.2412.06598,
title = {Gravitational capture cross-section in Zipoy-Voorhees spacetimes},
author = {Serzhan Momynov and Kuantay Boshkayev and Hernando Quevedo and Farida Belissarova and Anar Dalelkhankyzy and Aliya Taukenova and Ainur Urazalina and Daniya Utepova},
journal= {arXiv preprint arXiv:2412.06598},
year = {2024}
}