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

TL;DR

This paper extends the vacuole model to include a cosmological constant and explores light deflection, confirming previous results and introducing new local coupling terms, with implications for dark matter and gravity theories.

Contribution

It introduces new terms in the second order light deflection calculations within the vacuole model and compares different methods for incorporating cosmological constant and Weyl gravity effects.

Findings

Confirmed light bending in vacuole model with cosmological constant.

Derived new local coupling term involving {\Lambda} in light deflection.

Compared effects of Weyl gravity parameter {\gamma} with dark matter properties.

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 -((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.