Correspondence between two gravitational lens equations in a static and spherically symmetric spacetime
Year: 2025
Type: letter
Abstract: Virbhadra and Ellis have proposed a very accurate equation (referred to as the VE equation) for the gravitational lens in a static and spherically symmetric spacetime [Phys. Rev. D 62, 084003 (2000)], whereas an improved equation (referred to as the OB equation) has been derived by Bozza [Phys. Rev. D 78, 103005 (2008)] based on a relation found by Ohanian [Am. J. Phys. 55, 428 (1987)]. The OB equation was rediscovered later by Takizawa et al. [Phys. Rev. D 102, 064060 (2020)]. The VE and OB equations seem to be very different from each other. The present paper shows that there exists an unphysical branch in the VE equation. Consequently, the VE equation can be improved by removing the unphysical branch. The improved version of the VE equation is found to be the same as the OB equation when a suitable transformation is made between the deflection angles defined differently in the two formulations. An explicit expression of the transformation is found. We also argue possible numerical differences when the transformation between the deflection angles is ignored.
Authors: Ryuya Kudo, Hideki Asada
Institution: Hirosaki University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407193042