Theoretical Aspects of Gravitational Lensing in TeVeS

Since Bekenstein's (2004) creation of his Tensor-Vector-Scalar theory(TeVeS), the Modified Newtonian dynamics (MOND) paradigm has been redeemed fromthe embarrassment of lacking a relativistic version. One primary success ofTeVeS is that it provides an enhancement of gravitational lensing, which couldnot be achieved by other MONDian theories. Following Bekenstein's work, weinvestigate the phenomena of gravitational lensing including deflection angles,lens equations and time delay. We find that the deflection angle would maintainits value while the distance of closest approach vary in the MOND regime, thiscoincides with the conclusion of Mortlock and Turner's (2001) intuitionalapproach. Moreover, the scalar field, which is introduced to enhance thedeflection angle in TeVeS, contributes a negative effect on the potential timedelay. Unfortunately this phenomenon is unmeasurable in lensing systems wherewe can only observe the time delay between two images for a given source.However, this measurable time delay offers another constraint on the mass ratioof the DM and MOND scenarios, which in general differs from that given by thedeflection angle. In other words, for a lensing system, if two masses, m_gN andm_gM, are mutually alternatives for the deflection angles in their ownparadigm, regarding the time delay they are in general in an exclusiverelation.Comment: 15 pages, 7 figure