Neutron stars in Starobinsky model

TL;DR

This paper investigates neutron star structures within the Starobinsky f(R) gravity model, revealing that matching conditions impose unnatural fine-tuning problems and challenge the model's physical plausibility for realistic astrophysical objects.

Contribution

The study provides an exact, non-perturbative analysis of neutron stars in the Starobinsky model, highlighting inherent fine-tuning issues and questioning the model's naturalness for describing compact stars.

Findings

Matching conditions are difficult to satisfy for some equations of state.

The model requires fine-tuning of boundary conditions at the star's center.

The results challenge the physical plausibility of the Starobinsky model for neutron stars.

Abstract

We study the structure of neutron stars in $f(R)=R+\alpha R^{2}$ theory of gravity (Starobinsky model), in an exact and non-perturbative approach. In this model, apart from the standard General Relativistic junction conditions, two extra conditions, namely the continuity of the curvature scalar and its first derivative needs to be satisfied. For an exterior Schwarzschild solution, the curvature scalar and its derivative has to be zero at the stellar surface. We show that for some equation of state (EoS) of matter, matching all conditions at the surface of the star is impossible. Hence the model brings two major fine-tuning problems: (i) only some particular classes of EoS are consistent with Schwarzschild at the surface and (ii) given that EoS, only a very particular set of boundary conditions at the centre of the star will satisfy the given boundary conditions at the surface. Hence we show that this model (and subsequently many other f(R) models where uniqueness theorem is valid) is highly unnatural, for the existence of compact astrophysical objects. This is because the EoS of a compact star should be completely determined by the physics of nuclear matter at high density and not the theory of gravity.