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<p>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 (<i>q</i>-metric), which is the simplest generalization of the Schwarzschild metric, containing an independent quadrupole parameter <i>q</i>. 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.</p>

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Gravitational capture cross-section in Zipoy-Voorhees spacetimes

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Serzhan Momynov,
  • Kuantay Boshkayev,
  • Hernando Quevedo,
  • Farida Belissarova,
  • Anar Dalelkhankyzy,
  • Aliya Taukenova,
  • Ainur Urazalina,
  • Daniya Utepova

摘要

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.