From matter density to deflection angle and gravitational lensing using a perturbative method
Year: 2025
Type: article
Abstract: In this work, we develop a perturbative method to compute the deflection angles of null or timelike signals in spacetimes filled with a static and spherically symmetric (SSS) perfect fluid with fairly arbitrary density distributions. After solving the Tolman–Oppenheimer–Volkoff equations, the metric functions of the spacetime are obtained either as asymptotic series or as expansions around a finite boundary. The deflection angles of null or timelike signals in the weak-field limit in such spacetimes can then be expressed as series expansions in terms of the impact parameter, with coefficients determined by the metric expansions and, in turn, by the density distribution function. Gravitational lensing equations are also solved perturbatively to derive the apparent angles of the lensed images. Comparing our perturbative formulas with numerical results demonstrates the validity and efficiency of our method and results. This procedure establishes a direct connection between the mass density, the deflection angles, and the apparent angles of gravitationally lensed images. We apply these methods and results to the generalized Navarro–Frenk–White model and some other density profiles to analyze the influence of the density parameters.
Source: Physics of the Dark Universe
Authors: Peiran Liu, Xiaotian Zhang, Junji Jia
Institution: Wuhan University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,660
Funder: Wuhan University
OpenAlex ID: W4414443697