Gravitational Collapse in Repulsive $R+\mu^4/R$ Gravity

TL;DR

This paper examines how the modified gravity theory $R+rac{ ext{ extmu}^4}{R}$ affects gravitational collapse of stars, highlighting the role of the parameter extmu and junction conditions in determining stellar evolution outcomes.

Contribution

It analyzes collapsing conditions in the $R+rac{ ext{ extmu}^4}{R}$ gravity model and explores the impact of junction condition violations on astrophysical predictions.

Findings

Collapse criteria depend on the parameter extmu.

Violating junction conditions leads to contradictions with standard predictions.

The theory's consistency is sensitive to extmu and junction condition satisfaction.

Abstract

In this paper we work out collapsing conditions for a spherical star in the weak field limit of the $R+\mu^4/R$ gravity and discuss the importance of the parameter $\mu$ to generate different criteria in the theory. Such criteria are proved to be resulting in a variety of different fates for the evolution of the outer shells of stars. Furthermore, we investigate the special case of violating the first junction condition and point out corresponding contradictions to the normal cases. These results show that the consistency of the $R+\mu^4/R$ theory of gravity with the common astrophysical predictions relies highly on the adoption of the parameter $\mu$ and satisfaction/violation of the first junction condition. For those anomalous results, further observational attempts are mandatory.