On static and spherically symmetric solutions of Starobinsky model

Abstract

We investigate the problem of static and spherically symmetric solutions in the Starobinsky gravity model. By extending the Lichnerowicz and Israel theorems, William Nelson has demonstrated that the Schwarzschild solution is the unique static, spherically symmetric and asymptotically flat black hole solution in the Starobinsky model. However, Hong Lü et al. find that there are sign errors in the proof of Nelson. This raises the problem of whether Nelson’s proof is correct or not. In order to answer this question, we explore the corresponding solutions by using the Taylor series expansion method. We find that Nelson’s conclusion is indeed correct despite the flaw in the proof.