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

Abstract

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 -((5πM^2Λ)/8) related to Λ, 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 Λ disappears from the path equation. However, the original Rindler-Ishak method (2007) still applies even if a certain parameter γ of Weyl gravity does not disappear. Here, using an alternative prescription, we obtain the known term -((γR)/2), as well as another new local term ((3πγM)/2) between M and γ. Physical implications are compared, where we argue that the repulsive term -((γR)/2) can be masked by the Schwarzschild term ((2M)/R) in the halo regime supporting attractive property of the dark matter.

15 pages

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