Weak gravitational deflection by two-power-law densities using the Gauss-Bonnet theorem

Karlo de Leon and Ian Vega
Phys. Rev. D 99, 124007 – Published 10 June 2019

Abstract

We study the weak deflection of light by nonrelativistic mass distributions described by two-power-law densities ρ(R)=ρ0Rα(R+1)βα, where α and β are non-negative integers. New analytic expressions of deflection angles are obtained via the application of the Gauss-Bonnet theorem to a chosen surface on the optical manifold. Some of the well-known models of this two-power-law form are the Navarro-Frenk-White (NFW) model (α,β)=(1,3), Hernquist (1,4), Jaffe (2,4), and the singular isothermal sphere (2,2). The calculated deflection angles for Hernquist and NFW agree with that of Keeton and Bartelmann, respectively. The limiting values of these deflection angles (at zero or infinite impact parameter) are either vanishing or similar to the deflection due to a singular isothermal sphere. We show that these behaviors can be attributed to the topological properties of the optical manifold, thus extending the pioneering insight of Werner and Gibbons to a broader class of mass densities.

  • Figure
  • Figure
  • Received 23 March 2019

DOI:https://doi.org/10.1103/PhysRevD.99.124007

© 2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Techniques
Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Karlo de Leon* and Ian Vega

  • National Institute of Physics, University of the Philippines, Diliman, Quezon City, 1101, Philippines

  • *kndeleon@nip.upd.edu.ph
  • ivega@nip.upd.edu.ph

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Issue

Vol. 99, Iss. 12 — 15 June 2019

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