Anisotropic compact stars in $f(R)$ gravity

TL;DR

This paper develops a new anisotropic neutron star model within $f(R)$ gravity, deriving interior solutions that satisfy physical and stability conditions, and matches observational data of pulsars.

Contribution

It introduces a novel interior solution for anisotropic compact stars in $f(R)$ gravity, ensuring physical viability and stability, and aligns with observational pulsar data.

Findings

The model satisfies energy and stability conditions.

It accurately matches observational pulsar data.

The solution remains physically consistent for compactness parameter $C << 0.5$.

Abstract

We derive a new interior solution for stellar compact objects in $f\mathcal{(R)}$ gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $f\mathcal{(R)}$. After, the time component of the metric potential and the form of $f(\mathcal R)$ function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter $C$ which has to be $C=2GM/Rc^2 <<0.5$ for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman-Oppenheimer-Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.