Vacuum solutions around spherically symmetric and static objects in Starobinsky model

Abstract

The vacuum solutions around a spherically symmetric and static object are studied in Starobinsky model with perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star. The modified vacuum solution leads to deviations from general relativity that could be measured in light bending observations.