On static and spherically symmetric solutions of Starobinsky model

TL;DR

This paper confirms that the Schwarzschild solution is the unique static, spherically symmetric, asymptotically flat black hole in the Starobinsky model, despite previous doubts about the proof's correctness.

Contribution

It verifies the uniqueness of Schwarzschild solutions in the Starobinsky model using Taylor series expansion, addressing doubts about earlier proofs.

Findings

Schwarzschild solution is unique in the Starobinsky model.

Nelson's conclusion holds despite proof flaws.

Taylor series expansion confirms solution uniqueness.

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 have demonstrated that the Schwarzschild solution is the unique static, spherically symmetric, and asymptotically flat black hole solution in the Starobinsky model. However, Hong L{\"u} et al find that there are sign errors in the proof of Nelson. This raises the problem 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.