Charged quark stars in metric $f(R)$ gravity

TL;DR

This paper derives modified TOV equations for charged quark stars in $f(R)$ gravity, analyzing how the quadratic Ricci scalar term influences their structure, mass, radius, and charge distribution.

Contribution

It introduces the first detailed study of charged quark stars within metric $f(R)$ gravity using the Starobinsky model and explores the effects of the $ ho_{ch}/ ho$ ratio and $eta$ parameter.

Findings

Radius decreases compared to GR at low densities

Mass at the surface decreases with increasing $oldsymbol{eta}$

Maximum total charge increases with the $oldsymbol{ extit{α}}$ parameter

Abstract

We provide the modified TOV equations for the hydrostatic equilibrium of charged compact stars within the metric $f(R)$ gravitational background. We adopt the MIT bag model EoS for the dense matter and assume a charge distribution where the electric charge density $\rho_{\rm ch}$ is proportional to the standard energy density $\rho$. Using the Starobinsky model, we explore the role of the $\alpha R^2$ term, where $\alpha$ is a free constant and $R$ the Ricci scalar, on the global properties of charged stars such as radius, mass and total charge. We present the dependence of the structure of the star for several values of $\alpha$ and for different values of the constant parameter $\beta\equiv \rho_{\rm ch}/\rho$. Remarkably, we find that the radius decreases with respect to its GR value for low central densities, while the opposite occurs in the high-central-density region. The mass measured at the surface always decreases and the maximum-total charge undergoes a substantial increase as the parameter $\alpha$ increases. We also illustrate the variations of the asymptotic mass as a consequence of the electric charge and the extra quadratic term.