[Paper Review] On white dwarfs and neutron stars in Palatini f(R) gravity

Vappu Reijonen|ArXiv.org|Dec 4, 2009

Geophysics and Gravity Measurements1 references3 citations

TL;DR

This paper investigates how Palatini f(R) gravity modifies the structure and maximum masses of white dwarfs and neutron stars by solving the field equations numerically for f(R) = R + αR² and f(R) = R − μ⁴/R using a Fermi gas equation of state. It finds that the Chandrasekhar and Tolman-Oppenheimer-Volkoff limits are significantly altered or vanish for α ≳ 10⁻¹⁶ m² and α ≳ 10⁻¹⁹ m², respectively, offering observational constraints on f(R) gravity models.

ABSTRACT

In Palatini $f(R)$ gravity, the parameters of the Schwarzschild - de Sitter solution as well as the whole interior solutions of compact objects are expected to change when compared to general relativity. We solve the Palatini field equations numerically in the case of the models $f(R) = R + αR^2$ and $f(R) = R - μ^4/R$, and using the equation of state of Fermi gas. We show how the density profiles and the prediction for the maximum masses of white dwarfs (the Chandrasekhar limit) and neutron stars (the Tolman-Oppenheimer-Volkoff limit) are altered, and thereby conclude that observations on compact stars may be used to exclude alternative gravity models.

Motivation & Objective

• To examine how Palatini f(R) gravity alters the internal structure and maximum masses of compact stars like white dwarfs and neutron stars.
• To test whether deviations from general relativity in strong-field regimes can be constrained by observations of compact star properties.
• To evaluate the viability of specific f(R) models—f(R) = R + αR² and f(R) = R − μ⁴/R—under stellar structure constraints.
• To assess whether the Chandrasekhar and Tolman-Oppenheimer-Volkoff limits are modified or disappear in these gravity models.
• To provide a foundation for future work using improved equations of state and observational data from binary systems and supernovae.

Proposed method

• Numerical solution of the Palatini f(R) field equations for two specific f(R) models: f(R) = R + αR² and f(R) = R − μ⁴/R.
• Use of a single-species spin-1/2 Fermi gas equation of state from core to surface of stars, simplifying the matter content for initial modeling.
• Implementation of the conformal connection relation Γ = {h} + correction terms, where hμν = Fgμν, to derive the effective metric and curvature profiles.
• Matching of interior solutions to the exterior Schwarzschild-de Sitter solution to ensure global consistency of the spacetime geometry.
• Calculation of the Schwarzschild mass as a function of radius to analyze mass-radius relations and stability curves.
• Analysis of the behavior of the metric function B(r) and the mass parameter m(r) to detect non-physical features like negative mass or horizon formation.

Experimental results

Research questions

• RQ1 How does the f(R) = R + αR² model affect the central density and maximum mass of white dwarfs compared to general relativity?
• RQ2 What is the impact of the f(R) = R − μ⁴/R model on neutron star structure, especially at high densities?
• RQ3 At what value of α does the Chandrasekhar limit disappear in the Palatini f(R) framework?
• RQ4 How does the Tolman-Oppenheimer-Volkoff limit shift with increasing α in the f(R) = R + αR² model?
• RQ5 Can the observed properties of compact stars rule out or constrain specific f(R) gravity models?

Key findings

• For f(R) = R + αR², the Chandrasekhar limit disappears when α ≳ 10⁻¹⁶ m², indicating a fundamental breakdown of the white dwarf mass limit in this gravity model.
• In the same model, the Tolman-Oppenheimer-Volkoff limit is reduced and appears to vanish for α ≳ 10⁻¹⁹ m², suggesting neutron stars may not collapse beyond a certain mass threshold.
• The density profiles of neutron stars become less centrally peaked with increasing α, indicating a softer effective equation of state in the modified gravity regime.
• For f(R) = R − μ⁴/R, no significant deviation from general relativity is observed unless μ⁴ >> 1 m⁻⁴, which is considered unnaturally large and thus excluded by physical constraints.
• The metric function B(r) exhibits non-physical behavior such as temporary negative mass parameter inside stars for α = 10⁻¹⁹ m², indicating potential instability or breakdown of the model at high densities.
• The stability curves of white dwarfs and neutron stars in Palatini f(R) gravity differ significantly from general relativity, offering a potential observational signature to constrain the parameter space of f(R) models.