Neutron stars in Palatini R+alpha R^2 and R+alpha R^2+beta Q theories

Georg Herzog,Hèlios Sanchis-Alepuz

doi:10.1140/epjc/s10052-021-09662-z

Abstract

We study solutions of the stellar structure equations for spherically symmetric objects in modified theories of gravity, where the Einstein-Hilbert Lagrangian is replaced by f(R)=R+alpha R^2 and f(R,Q)=R+alpha R^2+beta Q, with R being the Ricci scalar curvature, Q=R_{mu nu }R^{mu nu } and R_{mu nu } the Ricci tensor. We work in the Palatini formalism, where the metric and the connection are assumed to be independent dynamical variables. We focus on stellar solutions in the mass-radius region associated to neutron stars. We illustrate the potential impact of the R^2 and Q terms by studying a range of viable values of alpha and beta . Similarly, we use different equations of state (SLy, FPS, HS(DD2) and HS(TMA)) as a simple way to account for the equation of state uncertainty. Our results show that for certain combinations of the alpha and beta parameters and equation of state, the effect of modifications of general relativity on the properties of stars is sizeable. Therefore, with increasing accuracy in the determination of the equation of state for neutron stars, astrophysical observations may serve as discriminators of modifications of General Relativity.

Highlights

Quadratic curvature corrections are added to the Lagrangian [3]
We study solutions of the stellar structure equations for spherically symmetric objects in modified theories of gravity, where the Einstein-Hilbert Lagrangian is replaced by f (R) = R + α R2 and f (R, Q) = R + α R2 + β Q, with R being the Ricci scalar curvature, Q = Rμν Rμν and Rμν the Ricci tensor
As we will show in this paper, the changes in the mass-radius relation for neutron stars coming from the uncertainty in the equation of state (EoS) are sometimes comparable to the differences generated by the modifications of the gravity theory, which implies that if, in the future, reliable ab-initio calculations of the EoS were available, astrophysical observations could be used as discriminators for gravity theories

Summary

Introduction

In this paper we shall investigate the influence of two particular models of f (R) and f (R, Q) theories, namely f (R) = R + α R2 and f (R, Q) = R + α R2 + β Q on the mass-radius relation for neutron stars We study those theories in the Palatini formalism in which the dynamical degrees of freedom are the metric and the affine connection [11]. Note here that, when calculating R and Q from R(h) in f (R, Q), the Ricci tensor Rμν(h) must be contracted with the physical metric gμν, that is, via the matrix Bαν above [36]. Where σ1 and σ2 appear upon rewriting the matrix as ν α diag(σ1, σ2, σ2, σ2) from Eq (5) and are given by [36]

Equations of state

Results

Summary