Gravitational lensing by a dark compact object in modified gravity and observational constraints from Einstein rings

Abstract In this manuscript, we provide a comprehensive study of gravitational lensing by dark compact objects predicted by modified gravity (MOG) based on the scalar–vector–tensor action, with the aim of providing new insights into the nature of gravitational interactions. We compute weak and strong deflection angles for the specified static, spherically symmetric MOG spacetime. Additionally, we dedicate a section to exploring observational implications in the weak field limit. By employing a supermassive galactic black hole as a gravitational lens, we compare various parameters in MOG with those of the Schwarzschild black hole as lens in strong-field scenarios. Specifically, we model the black holes $${\text {M}87}{^*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mtext>M</mml:mtext> <mml:mn>87</mml:mn> </mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mmultiscripts> </mml:mrow> </mml:math> and $${\text {Sgr}}\, {\text {A}}{^*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>Sgr</mml:mtext> <mml:mspace/> <mml:mtext>A</mml:mtext> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mmultiscripts> </mml:mrow> </mml:math> as lenses within the MOG framework, calculating the corresponding lensing coefficients and distortion parameters in the weak field regime.