The Vacuole Model: New Terms in the Second Order Deflection of Light

The present paper is an extension of a recent work (Bhattacharya et al. 2010) to the Einstein-Strauss vacuole model with a cosmological constant, where we work out the light deflection by considering perturbations up to order M^3 and confirm the light bending obtained previously in their vacuole model by Ishak et al. (2008). We also obtain another local coupling term -((5{\pi}M^2{\Lambda})/8) related to {\Lambda}, in addition to the one obtained by Sereno (2008, 2009). We argue that the vacuole method for light deflection is exclusively suited to cases where the cosmological constant {\Lambda} disappears from the path equation. However, the original Rindler-Ishak method (2007) still applies even if a certain parameter {\gamma} of Weyl gravity does not disappear. Here, using an alternative prescription, we obtain the known term -(({\gamma}R)/2), as well as another new local term ((3{\pi}{\gamma}M)/2) between M and {\gamma}. Physical implications are compared, where we argue that the repulsive term -(({\gamma}R)/2) can be masked by the Schwarzschild term ((2M)/R) in the halo regime supporting attractive property of the dark matter.