Theoretical Aspects of Gravitational Lensing in TeVeS

Since Bekenstein's creation of his tensor-vector-scalar theory (TeVeS), the modified Newtonian dynamics (MOND) paradigm has been redeemed from the embarrassment of lacking a relativistic version. One primary success of TeVeS is that it provides an enhancement of gravitational lensing, which could not be achieved by other MOND theories. Following Bekenstein's work, we investigate the phenomena of gravitational lensing including deflection angles, lens equations, and time delay. We find that the deflection angle maintains its value, while the distance of closest approach varies in the MOND regime. We also use the deflection angle law to derive magnifications and investigate microlensing light curves. We find that the difference in the magnification of the two images in the point-mass model is not a constant, as in general relativity (GR). Besides, microlensing light curves could deviate significantly from GR in the deep MOND regime. Furthermore, the scalar field, which is introduced to enhance the deflection angle in TeVeS, contributes a negative effect on the potential time delay. Unfortunately, this phenomenon is unmeasurable in lensing systems, where we can only observe the time delay between two images for a given source. However, this measurable time delay offers another constraint on the mass ratio of the dark matter and MOND scenarios, which in general differs from that given by the deflection angle. In other words, for a lensing system, if two masses, m_gN and m_gM, are mutual alternatives for the deflection angles in their own paradigm, regarding the time delay they are in general in an exclusive relation.