Vacuum solutions around spherically symmetric and static objects in the Starobinsky model

TL;DR

This paper investigates vacuum solutions around static, spherically symmetric objects in the Starobinsky gravity model, revealing how higher-order terms influence the metric near the star and match Schwarzschild solutions at large distances.

Contribution

It introduces a perturbative method using matched asymptotic expansions to solve the modified field equations in the Starobinsky model, highlighting boundary layer effects.

Findings

Presence of a boundary layer near the star's surface due to higher-order terms.

The metric differs from Schwarzschild near the star depending on Ricci scalar boundary conditions.

Solutions match Schwarzschild metric at large distances from the star.

Abstract

The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a 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.