Dark stars in Starobinsky's model

TL;DR

This study investigates non-rotating dark stars within Starobinsky's $f(R)$ gravity model, revealing increased compactness and slightly higher maximum masses compared to General Relativity through numerical solutions.

Contribution

It introduces a numerical analysis of dark stars in Starobinsky's $f(R)$ gravity, considering bosonic dark matter as a Bose-Einstein condensate, and compares their properties to those in General Relativity.

Findings

Dark stars are more compact in $R+aR^2$ gravity.

Maximum star mass is slightly higher in the modified gravity.

Mass-to-radius relations vary with the parameter $a$.

Abstract

In the present work we study non-rotating dark stars in $f(R)$ modified theory of gravity. In particular, we have considered bosonic self-interacting dark matter modelled inside the star as a Bose-Einstein condensate, while as far as the modified theory of gravity is concerned we have assumed Starobinsky's model $R+aR^2$. We solve the generalized structure equations numerically, and we obtain the mass-to-ratio relation for several different values of the parameter $a$, and for two different dark matter equation-of-states. Our results show that the dark matter stars become more compact in the R-squared gravity compared to General Relativity, while at the same time the highest star mass is slightly increased in the modified gravitational theory. The numerical value of the highest star mass for each case has been reported.